A First Course in Probability
9th Edition
ISBN: 9780321794772
Author: Sheldon Ross
Publisher: PEARSON
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Chapter 5, Problem 5.7TE
The standard deviation of X. denoted SD(X), is given by
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Chapter 5 Solutions
A First Course in Probability
Ch. 5 - Let X be a random variable with probability...Ch. 5 - Prob. 5.2PCh. 5 - Prob. 5.3PCh. 5 - The probability density function of X. the...Ch. 5 - Prob. 5.5PCh. 5 - Compute E[X] if X has a density function given by...Ch. 5 - The density function of X is given by...Ch. 5 - The lifetime in hours of an electronic tube is a...Ch. 5 - Consider Example 4b &I of Chapter 4 &I, but now...Ch. 5 - Trains headed for destination A arrive at the...
Ch. 5 - A point is chosen at random on a line segment of...Ch. 5 - A bus travels between the two cities A and B....Ch. 5 - You arrive at a bus stop at 10A.M., knowing that...Ch. 5 - Let X be a uniform (0, 1) random variable. Compute...Ch. 5 - If X is a normal random variable with parameters...Ch. 5 - The annual rainfall (in inches) in a certain...Ch. 5 - The salaries of physicians in a certain speciality...Ch. 5 - Suppose that X is a normal random variable with...Ch. 5 - Let be a normal random variable with mean 12 and...Ch. 5 - If 65 percent of the population of a large...Ch. 5 - Suppose that the height, in inches, of a...Ch. 5 - Every day Jo practices her tennis serve by...Ch. 5 - One thousand independent rolls of a fair die will...Ch. 5 - The lifetimes of interactive computer chips...Ch. 5 - Each item produced by a certain manufacturer is,...Ch. 5 - Two types of coins are produced at a factory: a...Ch. 5 - In 10,000 independent tosses of a coin, the coin...Ch. 5 - Twelve percent of the population is left handed....Ch. 5 - A model for the movement of a stock supposes that...Ch. 5 - An image is partitioned into two regions, one...Ch. 5 - a. A fire station is to be located along a road of...Ch. 5 - The time (in hours) required to repair a machine...Ch. 5 - If U is uniformly distributed on (0,1), find the...Ch. 5 - Jones figures that the total number of thousands...Ch. 5 - The lung cancer hazard rate (t) of a t-year-old...Ch. 5 - Suppose that the life distribution of an item has...Ch. 5 - If X is uniformly distributed over (1,1), find (a)...Ch. 5 - Prob. 5.38PCh. 5 - If X is an exponential random variable with...Ch. 5 - Prob. 5.40PCh. 5 - Find the distribution of R=Asin, where A is a...Ch. 5 - Let Y be a log normal random variable (see Example...Ch. 5 - The speed of a molecule in a uniform gas at...Ch. 5 - Show that E[Y]=0P{Yy}dy0P{Yy}dy Hint: Show that...Ch. 5 - Show that if X has density function f. then...Ch. 5 - Prob. 5.4TECh. 5 - Use the result that for a nonnegative random...Ch. 5 - Prob. 5.6TECh. 5 - The standard deviation of X. denoted SD(X), is...Ch. 5 - Let X be a random variable that takes on values...Ch. 5 - Show that Z is a standard normal random variable;...Ch. 5 - Let f(x) denote the probability density function...Ch. 5 - Let Z be a standard normal random variable Z and...Ch. 5 - Use the identity of Theoretical Exercises 5.5 .Ch. 5 - The median of a continuous random variable having...Ch. 5 - The mode of a continuous random variable having...Ch. 5 - If X is an exponential random variable with...Ch. 5 - Compute the hazard rate function of X when X is...Ch. 5 - If X has hazard rate function X(t), compute the...Ch. 5 - Prob. 5.18TECh. 5 - If X is an exponential random variable with mean...Ch. 5 - Prob. 5.20TECh. 5 - Prob. 5.21TECh. 5 - Compute the hazard rate function of a gamma random...Ch. 5 - Compute the hazard rate function of a Weibull...Ch. 5 - Prob. 5.24TECh. 5 - Let Y=(Xv) Show that if X is a Weibull random...Ch. 5 - Let F be a continuous distribution function. If U...Ch. 5 - If X is uniformly distributed over (a,b), what...Ch. 5 - Consider the beta distribution with parameters...Ch. 5 - Prob. 5.29TECh. 5 - Prob. 5.30TECh. 5 - Prob. 5.31TECh. 5 - Let X and Y be independent random variables that...Ch. 5 - Prob. 5.33TECh. 5 - The number of minutes of playing time of a certain...Ch. 5 - For some constant c. the random variable X has the...Ch. 5 - Prob. 5.3STPECh. 5 - Prob. 5.4STPECh. 5 - The random variable X is said to be a discrete...Ch. 5 - Prob. 5.6STPECh. 5 - To be a winner in a certain game, you must be...Ch. 5 - A randomly chosen IQ test taker obtains a score...Ch. 5 - Suppose that the travel time from your home to...Ch. 5 - The life of a certain type of automobile tire is...Ch. 5 - The annual rainfall in Cleveland, Ohio, is...Ch. 5 - Prob. 5.12STPECh. 5 - Prob. 5.13STPECh. 5 - Prob. 5.14STPECh. 5 - The number of years that a washing machine...Ch. 5 - Prob. 5.16STPECh. 5 - Prob. 5.17STPECh. 5 - There are two types of batteries in a bin. When in...Ch. 5 - Prob. 5.19STPECh. 5 - For any real number y define byy+=y,ify00,ify0 Let...Ch. 5 - With (x) being the probability that a normal...Ch. 5 - Prob. 5.22STPE
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardGiven pdf f (x) = 1.5x2 for −1< x < 1. Determine variance of X.arrow_forwardA random variable Y has a uniform distribution over the interval (?1, ?2). Derive the variance of Y. Find E(Y)2 in terms of (?1, ?2). E(Y)2 = Find E(Y2) in terms of (?1, ?2). E(Y2) = Find V(Y) in terms of (?1, ?2). V(Y) =arrow_forward
- The correlation between X and Y Select one or more: a. is the covariance squared b. cannot be negative since variances are always positive. c. is given by corr(X, Y) = cov(X,Y)/var(X)var(Y)cov(X,Y)/var(X)var(Y) d. can be calculated by dividing the covariance between X and Y by the product of the two standard deviationsarrow_forwardSuppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.03. Suppose that on a given day 10 patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: None of these E(X)=0.5 and V(X)=0.475 E(X)=0.4 and V(X)=0.384 E(X)=0.3 and V(X)=0.291arrow_forwardLet X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The covariance of x and y is 0.35. Let Z=4X – 5Y+2. What is the mean and variance of Z?arrow_forward
- Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.03. Suppose that on a given day io patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: E(X)=0.4 and V(X)=0.384 O None of these O E(X)=0.5 and V(X)=0.475 O E(X)=0.3 and V(X)=0.291arrow_forwardIf X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.arrow_forwardAssume that ξ has a rectangular distribution with the mean value E(ξ) = 0 and the variance V(ξ) = 12. Calculate P (ξ> 5).arrow_forward
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