Please do this step by step because the explanation is a huge part of the grade....
1. Suppose that the p.d.f. of a random variable X is as follows: for 0<x<2, for 0 〈 x 〈 2. r for 0<< f(x) = 0 otherwise. Let Y - X (2 - X). First determine the c.d.f. of Y, then find its p.d.f. (Hint: when computing c.d.f., plotting the function Y- X(2 - X) which may help. )
4. Let X have p.d.f. fx(1),-1 < 2. Find the p.d.f. of Y-X2
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Question 9. Given the c.d.f of a continuous random variable X as: 0 if x < 0 Fx(x)= x3 if 0 sxs1 1 otherwise Write down the p.d.f of X.
3,40 A random variable X has probability density function fx(x) = 1 0<x< 1. Find the probability density function of Y = 4x3 - 2.
7.695 points Save Answer QUESTION 4 Let the random variable X and Y have the joint p.d.f. for 0 < x < 1, 0 < y < 1, and 0 < x +y < 1 | 24cy f(x, y) = { lo otherwise Find E[X].
Problem 3. The random variable X has density function f given by 0, elsewhere (a) Assuming that 6 0.8, determine K (b) Find Fx(t), the c.d.f. of X (c) Calculate P(0.4 <X < 0.8)
4.3.2 The cumulative distribution func- tion of random variable X is 0 r<-1, Fx (x) = (z + 1)2-1 x < 1, r1 Find the PDF fx(a) of X
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0 < y < x < 1. Find Var(Y|X).
5. (28 points) A continuous random variable X has probability density function given by f(x) = 3x^2,0<x< 1 O otherwise (c) What is the c.d.f. of Y = X^2 - 1? What is the p.d.f. of Y = X^2 - 1?
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3) Two random variables X and Y have the following joint PDF fx(x, y) = 1zu(x)u(y) e “CI)-(3) Calculate: a) P (2<x<4, -1<Y<5); b) P (0<x< 00, -00<Y<-2).