Consider the following pmf: p(x)- .25 for x - 1, 2, 3, 4 Determine the variance...
Suppose a random variable X has a pmf p(x) = [3^(x-1)] / [4^x] , x = 1, 2, ... (a) Find the moment generating function of X. (b) Give a realistic example of an experiment that this random variable can be defined from its sample space. (c) Find the mean and variance of X.
Consider a random variable X with RX = {−1, 0, 1} and PMF P(X = −1) = 1/4 , P(X = 0) = 1/2 , P(X = 1) = 1/4 . a) Determine the moment-generating function (MGF) MX(t) of X. b) Obtain the first two derivatives of the MGF to compute E[X] and Var(X). Consider a random variable X with Rx = {-1,0,1} and PMF Determine the moment-generating function (MGF) Mx(t) of X b) Obtain the first two derivatives of...
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2, 3,..The moment generating function for this kind of random variable is M(t)Pe 1-(1-P)et. (a) What is E(X)? O p(1-P) 1-P (a) What is Var(x)? 1-p p2 p(1-P) O p(1-P) o -p
Consider the following PMF for a continus random variable f(x) = 0,25-Kx®2 Calculate K Calculate P(3<x<5) Calculate P(X <= 4) Calculate E(X) Calculate Var(X)
2. A discrete random variable X has the following pmf: p(x)| 1-8 30/4 θ/4 A random sample of size n 30 produced the following observations:
Current Attempt in Progress Consider the following discrete random distribution. X P(x) 0 .15 1 25 2 .25 3 25 4 .10 What is the variance of the distribution? 5.1 3.61 1.22 1.79 1.49
Question 1. A Discrete Distribution - PME Verify that p(x) is a probability mass function (pmf) and calculate the following for a random variable X with this pmf 1.25 1.5 | 1.7522.45 p(x) 0.25 0.35 0.1 0.150.15 (a) P(X S 2) (b) P(X 1.65) (c) P(X = 1.5) (d) P(X<1.3 or X 221) e) The mean (f) The variance. (g) Sketch the cumulative distribution function (edf). Note that it exhibits jumps and is a right continuous function.
Question 4. [5 marksi Let Xbe a random variable with probability mass function (pmf) A-p for -1, 2,... and zero elsewhere (whereq-1-p, 0 <p< (a) Find the moment generating function (mg ofX. C11 (b) Using the result in (a) or otherwise find the expected value and variance of X. C23 (c) Let X, X,., X, be independent random variables all with the pmf fix) above, and let Find the mgf and the cumulant generating function of Y.
X Y P(X,Y) 0 1 4.92 02 1. Consider the following PMF 666 1 1 1 1 2 3 Determine the entropy (in units of nats) of the marginals P(X) and P(Y). Details:
Consider a Gaussian random variable X with mean 8 and variance 3. Find z if P[X>10]=1- (phi)(Z)