Let y be a random variable with p(y) given in the accompanying table. find e(y ), e(1/y ), e(y 2 − 1), and v(y ). y 1 2 3 4 p(y) .4 .3 .2 .1

Answers

Answer 1
Final answer:

This answer pertains to the computation of expected and variance values for a discrete random variable y using its given probability distribution function. Relevant principles include multiplying each value of y with its corresponding probability and then summing the products for the expected value, and further operations for other expected values and variance.

Explanation:

The subject pertains to finding the expected and variance values of a discrete random variable y, based on its probability distribution function (PDF). In this case, we have four values for y (i.e., 1, 2, 3, and 4) with corresponding probabilities given as .4, .3, .2, and .1 respectively.

E(y) or the expected value of y is obtained by multiplying each value of y with its corresponding probability and then summing the products, according to the formula E(y) = Σ y*P(y).

e(1/y) is the expected value of the reciprocal of y, obtained similarly by multiplying each 1/y with its corresponding P(y) and summing up the products.

e(y 2 − 1) represents the expected value of y-squared minus one, obtained by squaring each y, subtracting one, multiplying with the corresponding P(y), and then adding the results.

Finally, for v(y) or the variance of y, one would first need to find the expected value of y-squared [E(y^2)], and then use the identity v(y) = E(y^2) - {E(y)}^2 to compute the variance.

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Related Questions

Given the sets
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {0, 1, 4, 7, 9}, and B = {0, 4, 5, 6, 7}, use De Morgan's Laws to find the indicated set. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
(A' ∩ B)'

Answers

Final answer:

We used De Morgan's laws to find the complement of the set formed by the intersection of the complement of A and B. We first found the complement of A, then the intersection of this set with B, and finally took the complement of this new set.

Explanation:

In set theory, De Morgan's laws relate the intersection and union of sets in a very elegant way. Here, (A' ∩ B)' represents the complement of the set formed by the intersection of the complement of A and B.

First, let's find A'. This is the set of all elements in U that are not in A. U = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } and A = { 0, 1, 4, 7, 9 } So, A' = { 2, 3, 5, 6, 8 }.

Now, let's find the intersection of A' and B, denoted by A' ∩ B. We have B = { 0, 4, 5, 6, 7 } so A' ∩ B = { 5, 6 }.

Finally, let's find the complement of this set, denoted by (A' ∩ B)'. This is the set of all elements in U that are not in A' ∩ B. So, (A' ∩ B)' = { 0, 1, 2, 3, 4, 7, 8, 9 }.

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Solve for x: 2|2x − 2| + 4 = 20.

x = 5, x = −3
x = 5, x = −5
x = 3, x = −3
x = −5, x = 3

Answers

Subtract 4 from both sides of the equation.
2|2x−2|=16Divide both sides of the equation by 2.
|2x−2|=8Set 2x-2 equal to positive and negative 8.
2x−2=8,2x−2=−8Solve both equations for x.
x=5,−3
2|2x − 2| + 4 = 20.
2|2x − 2|  = 20.- 4
2|2x − 2| = 16
|2x − 2| =8

That means:
1st: 2x-2 = 8   and 2nd: 2x - 2 = -8
1st: 2x=10 and x = 5

2nd  2x-2=-8, 2x = -6 and x = -3

So x = 5 and x = -3 (1st answer)

what is the slope of the line that passes through each pair of points A(-2, -4), B(2,4)

Answers

the slope is 2 hope this helps

Prime factorization practice all factors 1.- 25 2.- 49 3.- 7 4.- 13 5.- 24 6.- 48 7.- 168

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I'll do the first 2 and 6, and I challenge you to do the other three on your own!

For 1, from some guess and check we can figure out that 5*5=25. Since 5 is a prime number, that's it!

For 2, we can figure out that 7*7=49 and 7 is a prime number, so we're good there.

From 6, we can do some guess and check to figure out that 2*24=48, 2*12=24, 2*6=12, and 2*3=6, resulting in 2*2*2*2*3=48 since 2 and 3 are prime numbers. We found out, for example, to find 2*12 due to that if 2*24=48, 2*24 is our current factorization. By finding 2*12=24, we can switch it to 2*2*12

Round 9.77 to the nearest tenth

Answers

9.77 to the nearest tenths

first, find the number that is in the tenths place....it is 7....now look at the number directly to the right of it....if that number is 5 or greater, u would round that 7 up to an 8...but if that number is 4 or below, ur 7 would stay the same.
So the number directly to the right of 7 is 7...and since it is greater then 5, u have to round the 7 in the tenths place up to 8.

solution is : 9.8

How to write 5x923 in expanded form

Answers

923 x 5 = 4615

4000 + 600 + 10 + 5 is your answer

hope this helps

or if you want the equation

(900 + 20 + 3) x 5

hope this helps
One way to do this would be to calculate 5(900) + 5(20) + 5(3).

4500 + 100 + 15 = 4615.

A bird of species A, when diving, can travel 6 times as fast as bird of species B top speed. if the total speeds for these to birds 231 miles per hour, find the fastest speed of the birds of species A and the fastest speed of the bird of species B

Answers

x=266/7
x=38mph b
6x=228mph a

rewrite vertically,then add
63,594+98,697+59,835

Answers

Hello! When all of these numbers are added together, the sum is 222,126. Here’s the problem written vertically to show my work.
  2221
  63594 
  98697
+59835
----------
222126


222126   is your answer

hope this helps

Clarence solved the equation 3x + 15 = 33 and showed the following work. 3x + 15 = 33 3x + 15 - 15 = 33 3x = 33 = x = 11 Which of the following is true? x is 11. x should be 6. x should be 16. x should be 99.

Answers

3x + 15 = 33
3x = 33 - 15
3x = 18
x = 18/3
x = 6 <==

Answer:

x=6

Step-by-step explanation:

At a harvest 16 ears of corn are being picked for every 18 peppers if 9 peppers have been picked how many ears of corn have been picked(I need the actual math)

Answers

16:18
 x : 9

x = 8

Hope this helps!

what is the complement to a 32 angle

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Complement of angle 32 degree is the angle which when added with 32 will yield 90 degree. Similarly the complement of angle 58 degree is 32 degree. In a right angled triangle, the two angles other than 90 degree are complement to each other.
2 angles are comlementary if they add to 90
so if x and y are complentary then x+y=90


the complemnt to a 32 degree angle is
32+x=90
minus 32 both sides
x=58 degres

the complement is 58 degrees

What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept?

Answers

y=-(3/5)x-7is the anwser because this is the form y=mx+b where m=5/3 any line perpendicular to this given line will have the slope of -1/m so, in this case slope of perpendicular is: -1/(5/3) = -3/5 we know the y-intercept is -7, point (0, -7) so wave: y = -(3/5)x - 7

Answer:

The slope is -3/2 and contains the point (0, −2). Which is b.

Step-by-step explanation:

(-3,-4) (3, 0)

slope = (0 +4) / (3 + 3) = 4/6 = 2/3

perpendicular so slope = -3/2

line on graph

y = mx + b

0 = 2/3 (3) + b

0 = 2+ b

b = -2

y intercept (0,-2)

The large rectangle's dimensions are three times the dimensions of the small rectangle. It is #60
A.)
B.)
C.)
D.)
I need help please

Answers

A. Larger rectangle is 3 times bigger in perimeter.
B. Larger rectangle is 9 time bigger in area.
C. The answers are not the same because the scale factor is 3, then the perimeter of large rectangle would have a perimeter 3 times bigger than the small one. Also, the area would be found by taking the scale factor of 3 and squaring it 3^2=9 since it is a square unit.
D. What happens is that now we have a scale factor of 2 so the perimeter would be 2 times bigger for the larger rectangle and the area would be 2^2=4 times bigger than the small one.
Final answer:

The large rectangle's dimensions are 3 times the dimensions of the small rectangle. If the small rectangle's dimensions are W for width and L for length, then the large rectangle's dimensions are 3W and 3L.

Explanation:

The subject of this question is Mathematics, specifically relating to geometry and ratios. You're asked to compare two rectangles: a large one and a small one. The large rectangle's dimensions (both the width and length) are three times the dimensions of the small rectangle. Let's assume the dimensions of the small rectangle are W (width) and L (length). Then, the dimensions of the large rectangle would be 3W and 3L, respectively. This is because the large rectangle is three times the size of the small rectangle in both width and length.

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Mr. Abernathy bought a selection of wrenches for his shop and paid $78. He bought the same number of $1.50 and $2.50 wrenches, and half of that number of $4 wrenches. The number of $3 wrenches is one more than the number of $4 wrenches. How many of each did he buy?

Answers

x = # of $4 wrenches 
2x = # of $1.50 wrenches 
2x = # of $2.50 wrenches 
x+1 = # of $3 wrenches 

x(4.00) + 2x(1.50) + 2x(2.50) + (x+1)(3.00) = $78 
4x + 3x + 5x + 3x + 3 = 78 
15x + 3 = 78 
15x = 75 
x = 5 

Therefore, he has 5 $4 wrenches, 10 $1.50 wrenches, 10 $2.50 wrenches and 6 $3 wrenches. 
Verify: 
5($4) + 10($1.50) + 10($2.50) + 6($3) = $20 + $15 + $25 + $18 = $78

In this algebraic word problem, equations were set up based on the prices and relationships between the numbers of wrenches bought, leading to the discovery that Mr. Abernathy purchased 12 wrenches each at $1.50 and $2.50, 6 wrenches at $4, and 7 wrenches at $3 to make a total of $78.

Mr. Abernathy's allocation of his $78 budget on wrenches can be formulated as an algebraic word problem where we define the number of wrenches bought at each price point and the total cost. Let us denote x as the number of $1.50 wrenches and also the number of $2.50 wrenches, so the number of $4 wrenches is x/2 since it is half of that number.

The number of $3 wrenches is x/2 + 1 because it is one more than the number of $4 wrenches. The total amount spent can be expressed as the sum of the products of the numbers of wrenches and their respective prices, which must equal $78.

The equation for the total amount spent on wrenches is therefore:

1.50x + 2.50x + 4(x/2) + 3(x/2 + 1) = 78

Solving this equation for x gives us the number of $1.50 and $2.50 wrenches, and then we can infer the quantities of the $4 and $3 wrenches.

After simplifying the equation, we solve for x, and by plugging x back into the previous expressions, we find out that Mr. Abernathy bought 12 wrenches at $1.50 each, 12 wrenches at $2.50 each, 6 wrenches at $4 each, and 7 wrenches at $3 each.

In discus competition an athlete threw the discus 63.37meters 62.95 meters and 63.7meters order the distance from least to greatest

Answers

62.95meters, 63.37meters, 63.7meters.
the answer to this question is 62.95,63.37,63.7

g(x) = x3 + 6x2 + 12x + 8

Determine the function’s value when x = −1.

Answers

Plugging -1 in for 1, we get (-1)^3+6(-1)^2+12*(-1)+8. For (-1)^3, since 3 is odd and -1 is negative, we end up with -1. For (-1)^2, since 2 is even, we end up with 1. For -1, we have -1, so we have (-1)+6*1+12*(-1)+8=-1+6-12+8=15-12=3

The temperature changed from 5C at 6 p.m. to -2C at midnight. How much did the temperature decrease?

Answers

Salutations!

The temperature changed from 5°C at 6 p.m. to -2°C at midnight. How much did the temperature decrease?

Lets solve this!

To find out how much the temperature is decreased, you need to subtract 5°°C from -2° C. from . 

Lets form this into statements ---

Temperature at 6 PM = 5°C

Temperature at midnight = -2°C.

Temperature decreased = 5°C - 2°C = 3° C.

3°C is the temperature decreased. 

Hope I helped (:

Have a great day!

from 5 to 0 is a 5 degree change

then from 0 to -2 is a 2 degree change

5+2 = 7 degree change overall

A store manager orders T-shirts so that 15 out of every 35 are a medium. How many medium T shirts would you expect to find when there are 126 T shirts on a rack

Answers

15/35 = x/126

use cross multiplication to get 35x=126(15)
35x=1890 x=1890/35

x=54

54 medium shirts

what is 69.12 rounded to the nearest tenth

Answers

your answer will be 69.1

Find the area of the region bounded by the given curves. y = 9x2 ln(x), y = 36 ln(x)

Answers

alrighty
find where they intersect

9x²ln(x)=36ln(x)
divide both sides by 9
x²ln(x)=4ln(x)
[tex]ln(x^{x^2})=ln(x^4)[/tex]
so
[tex]x^{x^2}=x^4[/tex]
so x=1 and and 2 (x can't be 0 or -2 because ln(0) and ln(-2) don't exist)

so intersect at x=1 and x=2
which is on top?

9(1.5)²ln(1.5)=20.25ln(1.5)
36ln(1.5)=36ln(1.5)
36ln(1.5) is on top
so

that will be
the area is
[tex] \int\limits^2_1 {36ln(x)-9x^2ln(x)} \, dx= [/tex]
[tex] [36x(ln(x)-1)-x^3(3ln(x)-1)]^2_1=[/tex]
[tex] 48ln(2)-29[/tex]

the area between the curves is 48ln(2)-29
Final answer:

The area of the region bounded by y = 9x2 ln(x) and y = 36 ln(x) is found by integrating the absolute difference of the two functions from x = 1 to x = 2, which yields ∫ from 1 to 2 (|36 ln(x) - 9x2 ln(x)|) dx.

Explanation:

To find the area of the region bounded by the curves y = 9x2 ln(x) and y = 36 ln(x), you first need to find the points where they intersect. This means setting the two functions equal to each other and solving for x, i.e., 9x2 ln(x) = 36 ln(x).

This simplifies to x2 = 4 which yields two solutions x = 2 and x = -2. However, since the natural logarithm ln(x) is not defined for x < 0, we discard x = -2. So, the two curves intersect at x = 2.

The area between the curves from x = 1 to x = 2 is then obtained by integrating the absolute difference of the two functions from x = 1 to x = 2, which gives:

∫ from 1 to 2 (|36 ln(x) - 9x2 ln(x)|) dx. You can evaluate this integral with standard calculus techniques.

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how many times larger is the value of the 5 in 95,284 than the value 5 in 8,521

Answers

the value of 5 in 95,284 is 5000
the value of the 5 in 8,521 is 500

5000/500 = 10

so the value of the 5 in 95,824 is 10 times greater then the value of the 5 in 8,521 

Write an expression for the following statement(s), and then list each operation
present (make sure you define any variables used).
A record company earns 25% of what a band collects in total sales. That
percentage is deducted from the band’s total sale

Answers

Let's assign variables for the unknowns. Let x be the amount of total sales while x is the amount of net sales. It is called net sales because a percentage is still deducted from it. The equation will be written as:

Net Sale = Total Sales - 0.25*Total Sales
y = x - 0.25x
y = 0.75x

Rico is estimating 139 x 18 Find his mistake and correct it.


100 x 10 =1,000

Answers

139 is suppose to be 140 and 18 is suppose to be 20, 140 x 20 = 2800
Home this works

An open top box with a square base has a surface area of 100 square inches. express the volume of the box as a function of the length of the edge of the base. what is its domain?

Answers

Let the base be a square of side length = a ft, and height h ft.

The box has a base of area: [tex]a \cdot a = a^2 (square ft) [/tex], 

and 4 lateral faces of area ah (square ft).


thus the total area of the box is [tex]a^2+4ah[/tex].

we can reduce the number of variables as follows:

[tex]a^2+4ah=100\\\\4ah=100-a^2\\\\h= \frac{100-a^2}{4a}= \frac{25}{a}- \frac{a}{4} [/tex]



The volume of the box is given by the function:

[tex]V(a)=a \cdot a \cdot (\frac{25}{a}- \frac{a}{4} )=25a- \frac{a^3}{4} [/tex].



To find the domain we solve 

[tex]25a- \frac{a^3}{4} \ \textgreater \ 0\\\\a(25- ( \frac{a}{2} )^{2} )\ \textgreater \ 0\\\\a(5- \frac{a}{2})(5+ \frac{a}{2} )\ \textgreater \ 0[/tex]


the roots of the expression are 0, 10 and -10.    Since the overall sign of the expression is negative, we have the following sign table:

++++++++++++(-10)----------(0)++++++++++(10)--------------------

thus the solution of the inequation is (-infinity, -10) union (0, 10)

but we have another condition: a>0, since each side must be positive.


combining these 2 conditions, we have the domain: (0, 10)


Answer:  [tex]V(a)=25a- \frac{a^3}{4}[/tex], Domain (0, 10)



The volume = 25x - ¹/₄x³ (in cubic inches)Its domain (0, 10)Further explanation

Given:

An open-top box with a square base has a surface area of 100 square inches.

Question:

Express the volume of the box as a function of the length of the edge of the base. What is its domain?

The Process:

Let the length of the edge of the base = x Let height = h

Part-1: The surface area

Let us arrange the equation to get the surface area of ​​the box with a square base. Recall that the box is without a lid and its surface area is 100 square inches.

[tex]\boxed{ \ Surface \ area = area \ of \ base + (4 \times area \ of \ rectangle) \ }[/tex]

[tex]\boxed{ \ x^2 + (4 \cdot x \cdot h) = 100 \ }[/tex]

[tex]\boxed{ \ x^2 + 4xh = 100 \ }[/tex]

From the above equation, we set it again so that "xh" is the subject on the left.

Both sides are subtracted by x².

[tex]\boxed{ \ 4xh = 100 - x^2 \ }[/tex]

Both sides are divided by 4.

[tex]\boxed{ \ xh = \frac{100 - x^2}{4} \ }[/tex] ... (Equation-1)

That is the strategy we have prepared.

- - - - - - - - - -

Part-2: The volume

[tex]\boxed{ \ Volume \ of \ the \ box = length \times width \times height \ }[/tex]

[tex]\boxed{ \ Volume = x \cdot x \cdot h \ }[/tex]

[tex]\boxed{ \ Volume = x^2h \ }[/tex] ...(Equation-2)

Substitution Equation-1 into Equation-2.

[tex]\boxed{ \ Volume = x(xh) \ }[/tex]

[tex]\boxed{ \ Volume = x \bigg( \frac{100 - x^2}{4} \bigg) \ }[/tex]

[tex]\boxed{ \ Volume = \frac{100x - x^3}{4} \ }[/tex]

[tex]\boxed{ \ Volume = 25x - \frac{1}{4}x^3 \ }[/tex]

Thus, an expression of the volume of the box as a function of the length of the edge of the base is [tex]\boxed{\boxed{ \ Volume = 25x - \frac{1}{4}x^3 \ }}[/tex]

- - - - - - - - - -

Part-3: The domain of volume

The value of volume must always be positive, i.e., V > 0.

[tex]\boxed{ \ 25x - \frac{1}{4}x^3 > 0 \ }[/tex]

Both sides are multiplied by 4.

[tex]\boxed{ \ 100x - x^3 > 0 \ }[/tex]

Both sides are multiplied by -1, notice the change in the sign of the inequality.

[tex]\boxed{ \ x^3 - 100x < 0 \ }[/tex]

[tex]\boxed{ \ x(x^2 - 100) < 0 \ }[/tex]

[tex]\boxed{ \ x(x - 10)(x + 10) < 0 \ }[/tex]

We get [tex]\boxed{ \ x = 0, \ x = 10, \ and \ x = - 10 \ }[/tex].

Since the values of x cannot be negative, x = -10 are promptly rejected. For x = 0 can be used as one of the domain limits.

Consider the test of signs:

x(x - 10) (x + 10) is negative to the left of x = 10, and positive to the right of x = 10 on the number line.

Examples of tests:

[tex]\boxed{ \ for \ x = 2 \rightarrow 2(2 - 10)(2 + 10) < 0 \ }[/tex][tex]\boxed{ \ for \ x = 11 \rightarrow 11(11 - 10)(11 + 10) > 0 \ }[/tex]

Remember this form above, [tex]\boxed{\ x(x - 10)(x + 10) < 0 \ }[/tex], the value of the test result must be negative (because < 0).

Thus, the domain of the volume is [tex]\boxed{ \ 0 < x < 10 \ }[/tex] or [tex]\boxed{ \ (0, 10) \ }[/tex]

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Keywords: an open-top box, with, a square base, has a surface area, 100 square inches, express, the volume, as a function, the length, edge, base, what, its domain, test of signs, substitution

Imagine a sphere. if the sphere is cut three times at right angles, the resulting pieces would be what fraction of the original sphere?

Answers

1/3 of the original piece

Renee hiked for 3 and 3/ 4 miles. After resting, Renee hiked back along the same route for 2 and 1 /4 miles. How many more miles does Renee need to hike to return to the place where she started? Represent your answer as a simplified mixed number, if necessary.

Answers

5 miles to go back to werw he started

Misty took a multiple choice test in science that had 50 questions. If the relationship between the number she got correct and the number she got incorrect is 7:3, and she got 9 incorrect, how many did she get correct?

Answers

In this case, the total number of questions in the test is 50. The possible outcome for the question would be answered wrong, answered correctly or not answered. To know the amount of the correct answer, you need to multiply the incorrect with correct/incorrect ratio. The equation would be:
correct answer: 9 answer * 7/3= 21 answer.

Then for this test misty has:
9 incorrect answer
21 correct answer
20 blank/ not answered

find the unit rate???

Answers

2500 kilobytes/ 5 minutes= 500 kilobytes per minute

Final answer: 500 kilobytes per minute

Answer:

500 kilobytes/ 1 min

Step-by-step explanation:

2,500 kilobytes/ 5 min

2,500 divide by 5 = 500 kilobytes

500 kilobytes/ 1 min

Ruben bought six new books for his collection. This increased his collection by 12%. How many books did he have before his purchases?

Answers

 20. Let x represent the amount of books he had:
x + 6 = 1.12x

Subtract x from both sides:
6 = 0.12x

Divide both sides by 0.12; x = 50

28. $6 + 0.025*$6 = $6 + $0.15 = $6.15


which of these is a geometric sequence?

Answers

a geometric sequence deals with multiplying...u have to multiply by a common number to get the next number

1/4 * 2 = 1/2
1/2 * 2 = 1
1 * 2 = 2
2 * 2 = 4

so ur geometric sequence is : 1/4, 1/2, 1, 2, 4...with a common ratio of 2
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