M 362K, Spring 03, Smith

Assignment for Friday, October 17


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 + bx2    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.