Quiz 4

You should use the inside front cover of the textbook as a cheat sheet.

Justify all answers with neat and organized work. Clearly indicate your answers. 20 points possible.

1. (4 pts.) If X has a Poisson distribution so that 8P(X=2)=P(X=3), find P(X=15).

2. (4 pts.) Flaws in a certain type of drapery material appear on the average of one in 200 square feet. If we assume the Poisson distribution, find the probability of exactly 3 flaws in 150 square feet.

3. (4 pts.) The p.d.f. of X is f(x)=(3-x)/2, 1 £ x £ 3, zero elsewhere.

(a) Sketch the graph of this p.d.f.

(b) Determine the formula for, and sketch the graph of, the cumulative distribution function (c.d.f.) of X.

4. (4 pts.) The p.d.f. of X is f(x)=(3-x)/2, 1 £ x £ 3, zero elsewhere. (Same p.d.f. as previous problem.)

(a) Find m.

(b) Find s².

5. (4 pts.) The p.d.f. of X is f(x)=(3-x)/2, 1 £ x £ 3, zero elsewhere. (Same p.d.f. as previous two problems.) Find each of these.

(a) m=p_0.50

(b) p_0.90