The lifetime in months of a certain part has a gamma distribution with α = θ = 2. A company buys three such parts and uses one until it fails, replacing it with a second part. When the latter fails, it is replaced by the third part. What are the mean and the variance of the total lifetime (the sum of the lifetimes of the three parts) associated with this situation?
Answer to relevant QuestionsLet X1 and X2 be independent random variables with respective binomial distributions b(3, 1/2) and b(5, 1/2). Determine (a) P(X1 = 2, X2 = 4). (b) P(X1 + X2 = 7). Let X equal the outcome when a fair four-sided die that has its faces numbered 0, 1, 2, and 3 is rolled. Let Y equal the outcome when a fair four-sided die that has its faces numbered 0, 4, 8, and 12 is rolled. (a) Define ...Generalize Exercise 5.4-3 by showing that the sum of n independent Poisson random variables with respective means μ1, μ2, . . . , μn is Poisson with mean μ1 + μ2 + · · · + μn. Let X equal the weight of the soap in a “6-pound” box. Assume that the distribution of X is N(6.05, 0.0004). (a) Find P(X < 6.0171). (b) If nine boxes of soap are selected at random from the production line, find the ...Let X equal the weight in grams of a miniature candy bar. Assume that μ = E(X) = 24.43 and σ2 = Var(X) = 2.20. Let X be the sample mean of a random sample of n = 30 candy bars. Find (a) E(X). (b) Var(X). (c) P(24.17 ≤ ...
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