1.A receiving depot receives a shipment of 100 generators, 5 of which are defective.

(b) Calculate

2. Suppose the density of

\(\displaystyle

f(x)=\frac{1}{4} xe^{-\frac{x}{2}} \quad x>0

\)

0 otherwise

Use the moment generating function to calculate Var (

3.

(a) Compute the joint density of

(b) Are

Four are selected at random without replacement for inspection. Let

*Y*

be the number of defectives.

(a) What is the probability mass function of

(a) What is the probability mass function of

*Y*?

(b) Calculate

*P*(1*≤ Y ≤*3).2. Suppose the density of

*X*is given by\(\displaystyle

f(x)=\frac{1}{4} xe^{-\frac{x}{2}} \quad x>0

\)

0 otherwise

Use the moment generating function to calculate Var (

*X*).3.

Let

*X*and

*Y*be independent normal random variables, each having parameters

*μ*and

*σ*2.

(a) Compute the joint density of

*A*=

*X*+

*Y*and

*B*=

*X − Y*.

(b) Are

*A*and*B*independent?
Last edited: