EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 10, Problem 10.5P
Use the inverse transformation method to present an approach for generating a random variable from the Weibull distribution
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Chapter 10 Solutions
EBK FIRST COURSE IN PROBABILITY, A
Ch. 10 - The following algorithm will generate a random...Ch. 10 - Prob. 10.2PCh. 10 - Give a technique for simulating a random variable...Ch. 10 - Present a method for simulating a random variable...Ch. 10 - Use the inverse transformation method to present...Ch. 10 - Give a method for simulating a random variable...Ch. 10 - Let F be the distribution functionF(x)=xn0x1 a....Ch. 10 - Prob. 10.8PCh. 10 - Suppose we have a method for simulating random...Ch. 10 - Prob. 10.10P
Ch. 10 - Use the rejection method with g(x)=1,0x1, to...Ch. 10 - Prob. 10.12PCh. 10 - Prob. 10.13PCh. 10 - Prob. 10.14PCh. 10 - Prob. 10.15PCh. 10 - Let X be a random variable on (0, 1) whose density...Ch. 10 - Prob. 10.1STPECh. 10 - Prob. 10.2STPECh. 10 - Prob. 10.3STPECh. 10 - If X is a normal random variable with mean and...Ch. 10 - Prob. 10.5STPE
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- Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?arrow_forwardThe input voltage to a rectifier is the continuous uniform (-1, 1) random variable U. The rectifier output is a random variable W defined by W = = g(U) = { ° U < 0 U U20 What is the variance of W?arrow_forwardLet us consider a discrete random variable having the pmf given by, PX(k) ={ (1/3) , k = 1 (2/3) , k = 2. 0 , k = 3 Calculate the moment generating function for X. Also get the values of its mean and variance.arrow_forward
- we are evaluating two random variables X and Y with probabilitydistribution equal to: p(x, y) = P (X =x ∩ Y =y) given by the table attatched. find the correlation between X and Y when you know the ecpectations E(X) 0.95 and E(Y) = 0.9 and the variance is V(X) = 0.747 and V(Y) = 0.69arrow_forwardThree zero mean, unit variance random variables X, Y, and Z are added to form a new random variable, W = X + Y + Z. Random variables X and Y are uncorrelated, X and Z have a correlation coefficient of 1/2, and Y and Z have a correlation coefficient of - 1/2. a) Find the variance of W. b) Find the correlation coefficient between W and X. c) Find the correlation coefficient between W and the sum of Y and Z.arrow_forwardDerive formulas for the mean and variance of a Poisson random variable with parameter λ using its MGF.arrow_forward
- Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a normal random variable with mean 1 and variance 4. Assume that X1 and X2 are independent. (a) What is the distribution of the linear combination Y = 2X1 + 3X2? (b) What is the distribution of the linear combination Y = X1 – X2?arrow_forwardLet X 1 be a normal random variable with mean 2 and variance 3 and let X 2 be a normal random variable with mean 1 and variance 4. Assume that X 1 and X 2 are independent.(a) What is the distribution of the linear combination Y = 2X 1 + 3X 2 ?(b) What is the distribution of the linear combination Y = X 1 − X 2 ?arrow_forwardLet X and Y be independent random variables with means x,y and variances o, oy. Find an expression for the correlation of XY and Y in terms of these means and variances.arrow_forward
- Let X1,...,Xn be iid random variables with expected value 0, variance 1, and covariance Cov [Xi,Xj] = ρ, for i≠j. Use Theorem of linearity of expectation to find the expected value and variance of the sum Y = X1 +...+Xn.arrow_forwardConsider the bivariate distribution for the random variables x and y. The expected value of a linear combination of x and y is E(ax + by) = aE(y) + bE(x) E(ax + by) = aE(x) − bE(y) E(ax + by) = aE(y) − bE(x) E(ax + by) = aE(x) + bE(y)arrow_forward(b) Consider a binomial random variable X with parameters n and p. Let Y = X/n be a new random. Show that the expected value of Y is p and the variance of Y is pq/n. If p(y) is the p. m. f. for Y, show that nY~b(n,p). What are the possible values that Y can take on?arrow_forward
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