Description

CS 70 Discrete Mathematics and Probability Theory

1 Pullout Balls
Suppose you have a bag containing six balls numbered 1,2,3,4,5,6.
(a) You perform the following experiment: pull out a single ball and record its number. What is the expected value of the number that you record?
(b) You repeat the experiment from part (a), except this time you pull out two balls together and record the product of their numbers. What is the expected value of the total that you record?
2 How Many Queens?
You shuffle a standard 52-card deck, before drawing the first three cards from the top of the pile. Let X denote the number of queens you draw.
(a) What is P(X = 0), P(X = 1), P(X = 2) and P(X = 3)?
(b) What do your answers you computed in part a add up to?
(c) Compute E(X) from the definition of expectation.
(d) Are the Xi indicators independent?
3 Head Count
Consider a coin with P(Heads)= 2/5. Suppose you flip the coin 20 times, and define X to be the number of heads.
(a) Name the distribution of X and what its parameters are.
(b) What is P(X = 7)?
(c) What is P(X≥ 1)? Hint: You should be able to do this without a summation.
(d) What is P(12 ≤X≤ 14)?