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4.2. One at a time, until the lock is opened (keys that do not work are disca before another is tried). Let A box contains five keys, only one of which will a lock. Keys are randomly selected and tried, Y be the number of the trial on v the lock is opened. a. Find the probability function for Y. b. Give the corresponding distribution function c.What is P(Y < 3)? P(Y < 3)? P(Y = 3)?

4.2. One at a time, until the lock is opened (keys that do not work are disca before another is tried). Let A box contains five keys, only one of which will a lock. Keys are randomly selected and tried, Y be the number of the trial on v the lock is opened. a. Find the probability function for Y. b. Give the corresponding distribution function c.What is P(Y < 3)? P(Y < 3)? P(Y = 3)?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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4.2. One at a time, until the lock is opened (keys that do not work are discarded before another is tried). Let A box contains five keys, only one of which will open a lock. Keys are randomly selected and tried, Y be the number of the trial on which the lock is opened. a. Find the probability function for Y. b. Give the corresponding distribution function c.What is P(Y < 3)? P(Y < 3)? P(Y = 3)? %3D d If Y is a continuous random variable, we argued that, for all -00 < a < o, P(Y = a) = 0. Do any of your answers in part (c) contradict this claim? Why? %3D 4.38 Suppose that Y has a uniform distribution over the interval (0, 1). a. Find F(y). b. Show that P(a <Ys a + b), for a 2 0, b 2 0, and a + b<1 depends only upon the value of b 4.51. The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. What is the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 55 minutes? 4.52. Refer to Exercise 4.51. Find the mean and variance of the cycle times for the trucks. 4.53 The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific eight-hour day, one defective circuit board was found. a. Find the probability that it was produced during the first hour of operation during that day. b. Find the probability that it was produced during the last hour of operation during that day. c. Given that no defective circuit boards were produced during the first four hours of operation, find the probability that the defective board was manufactured during the fifth hour. .R F .r. 4.28 The proportion of time per day that all checkout counters in a supermarket are busy is a random variable Y with density function cy*(1 – y)*, 0< y < 1, 0, elsewhere. a Find the value of c that makes f(y) a probability density function. b Find E(Y).
Transcribed Image Text:4.2. One at a time, until the lock is opened (keys that do not work are discarded before another is tried). Let A box contains five keys, only one of which will open a lock. Keys are randomly selected and tried, Y be the number of the trial on which the lock is opened. a. Find the probability function for Y. b. Give the corresponding distribution function c.What is P(Y < 3)? P(Y < 3)? P(Y = 3)? %3D d If Y is a continuous random variable, we argued that, for all -00 < a < o, P(Y = a) = 0. Do any of your answers in part (c) contradict this claim? Why? %3D 4.38 Suppose that Y has a uniform distribution over the interval (0, 1). a. Find F(y). b. Show that P(a <Ys a + b), for a 2 0, b 2 0, and a + b<1 depends only upon the value of b 4.51. The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. What is the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 55 minutes? 4.52. Refer to Exercise 4.51. Find the mean and variance of the cycle times for the trucks. 4.53 The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific eight-hour day, one defective circuit board was found. a. Find the probability that it was produced during the first hour of operation during that day. b. Find the probability that it was produced during the last hour of operation during that day. c. Given that no defective circuit boards were produced during the first four hours of operation, find the probability that the defective board was manufactured during the fifth hour. .R F .r. 4.28 The proportion of time per day that all checkout counters in a supermarket are busy is a random variable Y with density function cy*(1 – y)*, 0< y < 1, 0, elsewhere. a Find the value of c that makes f(y) a probability density function. b Find E(Y).
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