Consider two independent continuous random variables X1, X2 each uniformly distributed over [0, 2]. Let Y = max (X1, X2), i.e., the maximum of these two random variables. Also, let Fy (y) be the cumulative distribution function (CDF) of Y. Find Fy (y) where y = 0.72.

Answers

Answer 1

The CDF of Y evaluated at y = 0.72 is 0.1296.

Since X1 and X2 are independent and uniformly distributed over [0, 2], their joint density function is:

f(x1, x2) = 1/4, for 0 ≤ x1 ≤ 2 and 0 ≤ x2 ≤ 2

To find the CDF of Y, we can use the fact that:

Fy(y) = P(Y ≤ y) = P(max(X1, X2) ≤ y)

This event can be split into two cases:

X1 and X2 are both less than or equal to y:

In this case, Y will be less than or equal to y.

The probability of this occurring can be calculated using the joint density function:

P(X1 ≤ y, X2 ≤ y) = ∫0y ∫0y f(x1, x2) dx1 dx2

= ∫0y ∫0y 1/4 dx1 dx2

[tex]= (y/2)^2[/tex]

[tex]= y^2/4[/tex]

One of X1 or X2 is greater than y:

In this case, Y will be equal to the maximum of X1 and X2.

The probability of this occurring can be calculated as the complement of the probability that both X1 and X2 are less than or equal to y:

P(X1 > y or X2 > y) = 1 - P(X1 ≤ y, X2 ≤ y)

[tex]= 1 - y^2/4[/tex]

Therefore, the CDF of Y is:

Fy(y) = P(Y ≤ y) = P(max(X1, X2) ≤ y)

= P(X1 ≤ y, X2 ≤ y) + P(X1 > y or X2 > y)

[tex]= y^2/4 + 1 - y^2/4[/tex]

= 1, for y ≥ 2

[tex]= y^2/4,[/tex]for 0 ≤ y ≤ 2

To find Fy(0.72), we simply substitute y = 0.72 into the expression for Fy(y):

[tex]Fy(0.72) = (0.72)^2/4 = 0.1296[/tex]

For similar question on probability.

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Answer 2

Since X1 and X2 are uniformly distributed over [0, 2], their probability density functions (PDFs) are:

fX1(x) = fX2(x) = 1/2, for 0 <= x <= 2

To find the CDF of Y = max(X1, X2), we need to consider two cases:

1. If y <= 0, then Fy(y) = P(Y <= y) = 0

2. If 0 < y <= 2, then Fy(y) = P(Y <= y) = P(max(X1, X2) <= y)

We can find this probability by considering the complementary event, i.e., the probability that both X1 and X2 are less than or equal to y. Since X1 and X2 are independent, this probability is:

P(X1 <= y, X2 <= y) = P(X1 <= y) * P(X2 <= y) = (y/2) * (y/2) = y^2/4

Therefore, the CDF of Y is:

Fy(y) = P(Y <= y) =

0,          y <= 0

y^2/4,      0 < y <= 2

1,          y > 2

To find Fy(0.72), we substitute y = 0.72 into the CDF:

Fy(0.72) = 0.72^2/4 = 0.1296

Therefore, the value of Fy(y) at y = 0.72 is 0.1296.

Learn more about cumulative distribution function (CDF) here: brainly.com/question/31961014

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Related Questions

solve the equation r4·r3 = _____

Answers

r12 because you multiply the numbers but keep the (r)

Jonathan says that when you add 7 2 3 to 2 2 3 , you must add the whole numbers together first ( 7 + 2 = 9 ). Then you just add the numerators together ( 2 + 2 = 4 ), and you add the denominators together ( 3 + 3 = 6 ). So the answer is 9 4 6 . Unfortunately, Jonathan's strategy is incorrect. Solve this problem, and then briefly explain the flaw in Jonathan's reasoning.

Answers

Answer:

9 4/3

Step-by-step explanation:

Jonathan working:

Add 7 2/3 to 2 2/3

Step 1: you must add the whole numbers together first ( 7 + 2 = 9 ).

Step 2: Then you just add the numerators together ( 2 + 2 = 4 ),

Step 3: you add the denominators together ( 3 + 3 = 6 ).

Step 4: Answer is 9 4/6

Correct workings:

Add 7 2/3 to 2 2/3

Step 1: you must add the whole numbers together first ( 7 + 2 = 9 ).

Step 2: Then you just add the numerators together ( 2 + 2 = 4 ),

Step 3: you pick one of the denominators because they are the same (3)

Step 4: Answer is 9 4/3

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Answers

Answer: x=18

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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what 20,000 divided by 24 ?

Answers

Answer:

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Step-by-step explanation:

hope this helps

Step-by-step explanation:

[tex]\qquad\sf\dashrightarrow 20000/24 [/tex]

[tex]\qquad\sf\dashrightarrow 10000/12 [/tex]

[tex]\qquad\sf\dashrightarrow 5000/6 [/tex]

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Find the value of 9x-5 given that – 2x-3=5.
Simplify your answer as much as possible.

Answers

Answer:

The value of 9x - 5 is -41.

Step-by-step explanation:

-2x - 3 = 5

-2x = 5 + 3

-2x = 8

x = -4

9x - 5

= 9(-4) - 5

= -36 - 5

= -41

A circular cylinder has a curved surface area 1320cm square and the radius of its base is 10.5cm find the height and volume of cylinder.​

Answers

Answer:

h=9.51

v=3293.89

Step-by-step explanation:

hope it helps :)

Answer:

h = 9.51

v = 3293.89

Step-by-step explanation:

please mark me as brainliest

PLS HELP 30 PTS!!!Use the coordinate plane to help you identify the length of each leg then use the Pythagorean Theorem to find the length of CD

Type your answer in the box.

Note: Type in only numeric part of the answer. Round your answer to the nearest hundredth.

Example: 12.70

Answers

Answer:

it says 15 points not 30

Step-by-step explanation:

Answer:

10.30

Step-by-step explanation:

Pythagorean Theorem is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].  The short leg(a) is 5 units long and the long leg(b) is 9 units long.  CD is the hypotenuse, the longest side (c).

[tex]5^{2}[/tex] +[tex]9^{2}[/tex] =[tex]c^{2}[/tex]

25+81=[tex]c^{2}[/tex]

106=[tex]c^{2}[/tex]

[tex]\sqrt{106}[/tex] = [tex]\sqrt{c^{2} }[/tex]

10.29563014 = c

Rounded to the nearest hundredth, 10.30

To check this is correct, the hypotenuse is the longest side, and 10.30 is longer than 5 and 9.  

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Answers

Answer:

20

Step-by-step explanation:

17+24+26+13=80

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Answers

Answer:

4/5

Step-by-step explanation:

That would be 1/5 + 3/5 which equals (1+3)/5 = 4/5


Mare has a monthly cell phone plan that has a fixed charge of $12 per month plus
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Answers

You need to multiply the cost per text message by the number of messages (x) add that to the fixed charge.

The total of those need to be less than or equal to the amount she wants to spend.

The equation would be written as:

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Suppose the radius of a circle is three units what is the circumference

Answers

Answer:

[tex]6\pi[/tex] or [tex]18.84[/tex] units

Step-by-step explanation:

The circumference of a circle can be found using the formula [tex]C=2\pi r[/tex], where [tex]C[/tex] is the circle's circumference and [tex]r[/tex] is the circle's radius. We know that [tex]r=3[/tex] and that we are solving for [tex]C[/tex]. Therefore:

[tex]C=2\pi r\\C=2*\pi *3\\C=6\pi[/tex]

Since [tex]\pi[/tex] is approximately [tex]3.14[/tex], [tex]6\pi =6*3.14=18.84[/tex] units. Hope this helps!

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Answers

Answer:

75.36 cm

Step-by-step explanation:

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Answers

Answer:

Horizontal

Step-by-step explanation:

Answer:

y = 9 is a horizontal line :)

Step-by-step explanation:

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wrong answers reported, correct answers get 5 stars

Answers

Answer:

10x + 35

Step-by-step explanation:

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5(2x) + 7(5)

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Write an equation and solve: At Trader Joes, Mrs.
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Answers

6.94-4.99= 1.95

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The Flightless Folly ship has 20 pirates aboard. 12 of those pirates wear an eye patch. What percentage of pirates wear an eye patch on the Flightless Folly?

Answers

60% of pirates wear an eye patch

Someone plz help me I wil give brainliest

Answers

Answer:

The answer is three quarters, one nickel's dime, and a penny!

Step-by-step explanation:

Answer:

Dime- 4

Penny- 1

Half Dollar- 1

Step-by-step explanation:

A dollar is 100 cents and you have 91

91- 50 (half dollar)= 41

41- 1 (one penny)= 40

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find the tangents of the acute angle in the right triangle. write each answer as a fraction​

Answers

Answer:

[tex]tanD=\frac{7}{24}[/tex]

[tex]tanF=\frac{24}{7}[/tex]

Step-by-step explanation:

We are given that

ED=24units

EF=7units

FD=25 units

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We know that

tangent=[tex]\frac{Perpendicular\;side}{Base}[/tex]

Using the formula

[tex]tanD=\frac{EF}{ED}[/tex]

[tex]tanD=\frac{7}{24}[/tex]

[tex]tanF=\frac{ED}{EF}[/tex]

[tex]tanF=\frac{24}{7}[/tex]

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Answers

Answer:

The answer will be -3

Step-by-step explanation:

Hope this Helped

Answer:

x= -3

Step-by-step explanation:

It is really Easy just Isolate the variable by dividing each factor that don't contain the variable

Over the course of 3 days, Calvin spent 10 hours delivering newspapers. He spent the same amount of time each day delivering newspapers. Which of the following equations represents the amount of time Calvin spent delivering papers each day?
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B: 10 ÷ 3 =
C:10 ÷ 7 =
D: 7 ÷ 10 =

Answers

I think the answer is d hope this help

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Answers

Given:

Triangle EFG is similar to triangle HIJ.

To find:

The measure of side IJ.

Solution:

We know that, corresponding sides of similar triangles are proportional.

Triangle EFG is similar to triangle HIJ.

[tex]\dfrac{EF}{HI}=\dfrac{FG}{IJ}[/tex]

Putting the given values, we get

[tex]\dfrac{7}{32}=\dfrac{4}{IJ}[/tex]

[tex]7\times IJ=4\times 32[/tex]

[tex]IJ=\dfrac{128}{7}[/tex]

[tex]IJ=18.2857[/tex]

[tex]IJ\approx =18.3[/tex]

Therefore, the measure of side IJ is 18.3 units.

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Answers

C it is C
I think hope this helps

expand the following: 4(2x + 1)

Answers

8x + 4 is the answer

Answer:

the equivalent expression is 8x + 4

Step-by-step explanation:

4(2x + 1) = 4x2 = 8 =

8x + 1 = 4x1 = 4 =

8x + 4

To check your work substitute 1

4(2(1) + 1) = 4(2 + 1) = 4(3) = 12

8(1) + 4 = 8+4 = 12

therefore they are both equivalent

hope this helped!

What is the complete factorization of the polynomial below? x3 + x2 + 4x + 4

Answers

Answer:

(x+1)(x+2/)(x-2/)

Step-by-step explanation:

Which point has the coordinates (2, 3)?
у
5
4
B.
С
3
2
D
A
1
0
1
2
з
4
х
5
ОА
ОС
OD
ОВ

Answers

Answer:

Point B

Step-by-step explanation:

The first number in the brackets is X while the second is Y (x, y).

X is the bottom line, while Y is the line going up.

Find 2 on the bottom line and 3 on the upright line. This gives us B.

I am sorry for the poor explanation.

find the fourth proportional to 2,3,6​

Answers

Answer:

9

Step-by-step explanation:

Let the fourth proportional be x Then

2 : 3 :: 6 : x

2/3 = 6 / x

2x = 3 * 6

x = 18 / 2

x = 9

Hope it will help :)

I need help with this question.

Answers

Answer:

[tex]13 {z}^{8} [/tex]

Step-by-step explanation:

20000 students took a standardized math test. The scores on the test are normally distributed, with a mean score of 85 and a standard deviation of 5. About how many students scored between 90 and 95?

Answers

Answer: 2718

Step-by-step explanation:

Given: Mean score = 85

Standard deviation = 5

Let x be the score of a random student that follows normal distribution.

Then, the probability that a student scored between 90 and 95 will be

[tex]P(90< x < 95)\\\\=P(\dfrac{90-85}{5}<\dfrac{x-\mu}{\sigma}<\dfrac{95-85}{5})\\\\= P(1< z< 2)\ \ \ \ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=P(z<2)-P(z<1)\\\\=0.9772-0.8413\\\\=0.1359[/tex]

The number of students scored between 90 and 95 = 0.1359 x (Total students)

= 0.1359 (20000)

= 2718

Hence, The number of students scored between 90 and 95 = 2718

The perimeter of a square is represented by the expression 32x-12. . Write two equivalent expressions for the perimeter and explain how to find the length of one side. x=3

Answers

Answer:

P = 2(l+w) ----------(1)

P = 4l----------- (2)

P= 32x- 12

4l = 32x- 12

l = 8x- 3

One side will be equal to 21 units and the perimeter will be 84 units when x=3.

Step-by-step explanation:

The perimeter is given by the formula

P = 2(l+w) ----------(1)

where p= perimeter , l= length and w= width.

But a square has the length equal to the width so w= l and the formula becomes

P = 2( l+l)

P = 2 (2l)

P = 4l----------- (2)

The perimeter of the square is

P= 32x- 12

or

4l = 32x- 12

dividing the whole equation by 4 we get

l = 8x- 3

So the length of one side can be obtained by dividing the perimeter by 4.

If x= 3

then

l= 8(3)-3

l= 24- 3

l = 21

One side will be equal to 21 units and the perimeter will be 84 units.

P = 4l = 4(21)= 84

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