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5. Determine a and Fx(x) for fx(x) given below. Determine Pr(-1 < X < 1) fx(x)...
6. For the probability assignment Pr(x = 1) = (3) ", i=1,2,.. determine: (a) Pr(X <3) (b) Pr(X > 4) (c) Fx(0)
If the probability density function of X is given by n2 for 1<x< 2 fx ) = 10 elsewhere (a) Find, E[X], E[X2], and E[X3] (b) Use your answer to part (a) to find E[X3 + 3X2 - 2x + 5)
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
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.
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
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
Question 13 The cumulative distribution function of X is given by Fx (x) = {-kr <0 0<x<2 > 2 Find (a) the value of k, (b) the probability density function fx (x), (c) the median of X, (d) the variance of X.
4. Let X have p.d.f. fx(1),-1 < 2. Find the p.d.f. of Y-X2
Additional Problem A: The CDF of random variable X is given by: I< -3 -3 < z< -2 Fx(r) = -2 <I< 2 a) Find the possible range of values that the random variable can take. b) Find E(X) = 4x, the expec ted value. c) Find P(X > 1). d) Find P(X > 1|X > -2).
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0 < y < x < 1. Find Var(Y|X).