Assignment:
Q1.) Let X be a discrete random variable with probability mass function Pr {X=k} = c(1+ k^2) for k= -2, -1, 0, 1, 2.
a) Determine c.
b) Determine Pr {X <= 0}
c) Determine the mean of X
d) Why is the previous answer fairly obvious?
e) Determine the variance of X
f) Compute Pr {X=2 | X >= 0}
g) Determine the moment generating function of X
Q2.) Let Y be a Poisson random variable with parameter 1.5
a) Compute Pr {Y=0}
b) Compute Pr {Y <= 1}
c) Compute Pr {Y=0 |Y <= 1}
d) What is E[Y]?
e) Determine the variance of Y
f) Determine the moment generating function
Q3) Suppose the random variable S has moment generating function of (q + p *(e^t))^n where q= 1- p, 0 < p < 1 and n is a positive integer. Find the mean and variance of Y.
Provide complete and step by step solution for the question and show calculations and use formulas.