Originally Posted by

**Ryan0710** 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 *Y* be the number of defectives. (a) What is the probability mass function of *Y *?

(b) Calculate *P*(1 *≤ Y ≤ *3).
[snip]

(a) Review the hypergeometric distribution.

(b) Pr(Y ≤ 3) - Pr(Y = 0).

Originally Posted by

**Ryan0710** [snip]

2. Suppose the density of *X *is given by f(x)=\frac{1}{4} xe^{-\frac{x}{2}} \quad x>0

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

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0 otherwise

Use the moment generating function to calculate Var (*X*).

[snip]

Apply the definition of the mgf. Use integration by parts to do the required integration. If you need more help, please show all yuor working and say where you are stuck.

Originally Posted by

**Ryan0710** [snip]

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?

(a) Use the Change of Variable Theorem. I assume you have been taught it. Where are you stuck?

(b) Can f(a, b) be written in the form g(a) h(b)?