If X has a moment generating function (mgf) as A) find the probability mass function of X. B) find the mean and variance of X by using the mgf, M(t), given in the photo C) what is P[X > 1|X > or equal to 0]

For the given probability density function, over the given interval, find the mean, the variance, and the standard deviation. 36) f(x)== // [12, 20] 36) B) μ = 16; o² = 5.33; o = 2.31 A) μ = 15.5; o2=5.20; o = 2.28 C) μ = 15; o2 = 5.34; o = 2.31 D) μ= 1.6; o2 = 5.24; o=2.29

The random variable U has the following distribution: U 123 PU(u) 0.20 0.40 0.40 (c) Write down the moment generating function (mgf) of U. (d) Use the mgf to help determine var[U].

Let X be a point randomly selected from the unit interval [0, 1]. Consider the random variable Y = (1-X)-¹/2 (a) Sketch Y as a function of X. (b) Find and plot the cdf of Y. (c) Derive the pdf of Y. (d) Compute the following probabilities: P(Y > 1), P(3 < Y < 6), P(Y ≤ 10).