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 + bx2 0≤ x ≤1
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.