u the percentage of students who ate taking exactly one of theses three courses. Random vector (X, Y) has the joint probability density function. (a) Find F(0.5, .75) = P(X <0.5,Y <0.75). %3D S 12(y – x)², 0, 0 < x < y < 1; - f (x, y) = { %3D elsewhere. (b) Find P(X > 1/4|Y = 3/4)

Q: Let F(r, y) = (1- e-*)(1 – e¬V), ±20, y20 be the cumulative density clion of two dimensional random…

A: Solution

Q: Let X and Y be two random variables having joint PDF f(e,y) = e-+, > 0, y> 0. W X and V = 2X+ 3F

A: The joint PDF of two random variables X and Y is,  f( x , y )  =   e-(x+y)    ; x&gt;0 , y &gt;00…

Q: (d) Are the random variables X and Y independent? Justify your answer.

A: To check independence of X and Y we have to find marginal pdfs of X and Y.

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A: Given that k=0.75 And the probability density function is, f(x)=e-2*0.75x+12e-0.75x, x&gt;0…

Q: If X is a uniformly distributed random variable in 2 find the density of 2 Y = tan X.

A: Answer: For the given data,

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Q: Q.3 The probability density function for a continuous random variable X is fe(8) = {* *o; Sa + bx²;…

A: Note: Since it is very long question. In each question there are multiple sub parts. I am answeing…

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Q: The distribution function of a RVX is given by F(x) = 1- (1+ x)e, x20. Find the density function,…

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Q: ndom variable X has cumulative distribution function F(x)given by 0. F(x) =- 6. +2x-2 , 2sxS3 1 x2 3

A: a. P(1&lt;X&lt;2.2) = F(2.2-) - F(1) = F(2.2) - F(1)  = -2.223+2*2.2-2 - 126 = 0.62

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Q: Q2 Let (X₁, X₂) be jointly continuous with joint probability density function e-(²₁+²2), x₁ > 0, x₂…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

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A: Problem can be solved using concept of expectation and variance. please find step by step solution…

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A: The Joint PDF of X and Y  is :f(x,y)=3x2+4y320≤x≤2,0≤y≤2

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Q: (a) Find c. (b) Let Z = (X + Y)−¹, find E[Z]. (c) Find the marginal distribution of X and Y.

A: Here we have given the joint probability density function of random variables X and Y. Using this we…