- Question 5 The Density Function Of A Random Variable X Is As Follows 0 X 1 1 X 1 X 0 Fx X 0 X 1 0 X 1 A Pro 1 (44.89 KiB) Viewed 22 times
Question 5 The density function of a random variable X is as follows: 0, x < -1 1+x, -1<x<0 fx(x) 0<x<1 0, x > 1 (a) Prove that the function fx(x) satisfies the conditions of a density function. (b) Find the cumulative distribution function of the distribution. X 3 (c) Find P(X < 0) and P(X>0). (d) Find P(-{< X < ). (e) Prove that the distribution is not symmetric, that is, it is not true that for all x > 0 we have P(X> x) = P(X <-X). Question 6 Assume that the density function of a random variable X is as follows: 0, X<-3, fx(x) 1/6, -3 < X <3, 0, x > 3. (a) What are the possible values of this random variable? (b) Find the probabilities P(X < 0) and P(X < 1). (c) Find P(X <0 X < 1).