Probability mass function and joint density
1.A receiving depot receives a shipment of 100 generators, 5 of which are defective.
Four are selected at random without replacement for inspection. Let
be the number of defectives.
(a) What is the probability mass function of
(b) Calculate P(1 ≤ Y ≤ 3).
2. Suppose the density of X is given by
Use the moment generating function to calculate Var (X).
X and Y be independent normal random variables, each having parameters μ and σ2.
(a) Compute the joint density of A = X + Y and B = X − Y .
(b) Are A and B independent?