Homework: Random Variable and Probability Distribution
Math 107 002
Homework 5 (due 13 Oct 2011)
Fall 2011
Please use your calculators and give your final answers to 3 significant figures. Show your work for full credit. Please state clearly all assumptions made.
1. Classify each random variable as discrete or continuous. (a) The number of visitors to the Museum of Science in Boston on a randomly selected day. (b) The camber-angle adjustment necessary for a front-end alignment. (c) The total number of pixels in a photograph produced by a digital camera. (d) The number of days until a rose begins to wilt after it is purchased from a flower shop. (e) The runnning time for the latest James Bond movie. (f) The blood alcohol level of the next person arrested for DUI in a particular county. 2. A bagel shop sells only two different types of bagels: plain (P) and cinnamon raisin (C). Five customers are selected at random. Past records have shown that the demand for cinnamon bagels is twice that for plain bagels. Each customer buys only one bagel and the experiment consists of recording what kind of bagel these five customers buy. Let the random variable X be the number of people who buy a plain bagel. (a) Find the probability distribution for X. (b) Suppose at least 3 people buy a plain bagel. What is the probability that exactly 4 people buy a plain bagel? 3. The probability distribution for a discrete random variable X is given by the formula p(r) = for r = 1, 2, . . . , 6. (a) Verify that this is a valid probability distribution. (b) Find P (X = 4). (c) Find P (X > 2). (d) Find the probability that X takes on the value 3 or 4. (e) Construct the corresponding probability histogram. 4. Two packages are independently shipped from Fort Collins, Colorado, to the same address in Seattle, Washington, and each is guaranteed to arrive within 4 days. The probability that a package arrives within 1 day is 0.10, within 2 days is 0.15, within 3 days is 0.25, and on the fourth day is 0.50. Let the random variable X be the total number of
Homework 5 (due 13 Oct 2011)
Fall 2011
Please use your calculators and give your final answers to 3 significant figures. Show your work for full credit. Please state clearly all assumptions made.
1. Classify each random variable as discrete or continuous. (a) The number of visitors to the Museum of Science in Boston on a randomly selected day. (b) The camber-angle adjustment necessary for a front-end alignment. (c) The total number of pixels in a photograph produced by a digital camera. (d) The number of days until a rose begins to wilt after it is purchased from a flower shop. (e) The runnning time for the latest James Bond movie. (f) The blood alcohol level of the next person arrested for DUI in a particular county. 2. A bagel shop sells only two different types of bagels: plain (P) and cinnamon raisin (C). Five customers are selected at random. Past records have shown that the demand for cinnamon bagels is twice that for plain bagels. Each customer buys only one bagel and the experiment consists of recording what kind of bagel these five customers buy. Let the random variable X be the number of people who buy a plain bagel. (a) Find the probability distribution for X. (b) Suppose at least 3 people buy a plain bagel. What is the probability that exactly 4 people buy a plain bagel? 3. The probability distribution for a discrete random variable X is given by the formula p(r) = for r = 1, 2, . . . , 6. (a) Verify that this is a valid probability distribution. (b) Find P (X = 4). (c) Find P (X > 2). (d) Find the probability that X takes on the value 3 or 4. (e) Construct the corresponding probability histogram. 4. Two packages are independently shipped from Fort Collins, Colorado, to the same address in Seattle, Washington, and each is guaranteed to arrive within 4 days. The probability that a package arrives within 1 day is 0.10, within 2 days is 0.15, within 3 days is 0.25, and on the fourth day is 0.50. Let the random variable X be the total number of