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1. A continuous random variable X has the following
2. Let X be a continuous random variable with density
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- Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let X be a random variable with pdf f(x) = kx*,-1Suppose a continuous random variable X has the probability density f(x) = K (1-x²) for 0 < x < 1, and f(x) = 0 otherwise. Find (i) K (ii) MeanSuppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?Suppose that therandom variable X has the probability density function c(1– x2) for -1s x <1 f(x) elsewhere What is the variance of X10) Let f(x) by the probability density function of some continuous random variable. Explain why it must be true that f(x) dx =1.Let X1, X2, X3 be independent Exp()-distributed random vairables. Determine the pdf of X(1)X(3)1. Let f be the probability density function of a continuous random variable X whose range is (-0, 00), where if a sxsb f(x) ={32 0 otherwise. (a) Explain why a, hence b, must be nonnegative. Graph the function f. (b) Find the value of b'-a. 7 (c) If it is known that P(X 8).Let X be a continuous random variable with the following PDF fx(=) = {** Į ce z 20 otherwise where c is a positive constant. a. Find c. b. Find the CDF of X, Fx(x). c. Find P(1 < X < 3).Suppose x and y are continuous random variables with joint pdf f(x,y)= 4(x-xy) if 0<x<1 and 0<y<1 and zero otherwise. What is probability p[X <Y ]Let X be a random variable with discrete pdf f(x) = x/8 if x = 1, 2, 5, and zero otherwise. Find: (a) E(X).7. Let X be a continuous random variable with probability density function given by Se-(2-z0) f (x) = x > x0 x < xo Find E(X).SEE MORE QUESTIONS