For each of the following distributions, verify the formulas for EX and Var X given in the text (a) Verify Var X if X has a Poisson () distribution (Compute EX(X 1) EX2 EX ) (b) Verify Var X if X has a negative binomial(r, p) distribution (c) Verify Var X if X has a gamma(, ) distribution (d) Verif...

a b where in the second equality we substituted y x 2 and in the third ...

For each of the following distributions, verify the formulas for EX and Var X given in the

Question:

For each of the following distributions, verify the formulas for EX and Var X given in the text.
(a) Verify Var X if X has a Poisson (λ) distribution. (Compute EX(X - 1) = EX2 - EX.)
(b) Verify Var X if X has a negative binomial(r, p) distribution.
(c) Verify Var X if X has a gamma(α, β) distribution.
(d) Verify EX and Var X if X has a beta(μ, σ) distribution.
(e) Verify EX and Var X if X has a double exponential (μ, a) distribution.