M 362K, Spring 03, Smith

## Assignment for Friday, October 17

TO HAND IN:

1. A sample of 3 items is selected at random from a box containing 20 items,
of which 4 are defective.

a. Find the probability mass function of the random variable
X = number of defective items in the sample.

b. Find the expected number of defective items.

2. The probability density function of the random variable X is given by

a + bx^{2} 0≤ x ≤1

f(x) =

0
otherwise

If E(X) = 2/5, find a and b. (Note: This is similar to but not exactly the
same as Problem 7 on p. 229)

3. Let X be a random number chosen from (1,e). (This means that X is uniformly
distributed on (1,e).) Find the expected value of 1/X.

4. Let A, B, and C be three events. Express the following events in terms
of A, B, and C, using intersections, unions, and complements as appropriate,
*and also* draw and shade in a Venn diagram showing the event.

a. At least two of A, B, C occur.

b. At most two of A, B, C occur.