The weekly demand X for propane gas (in thousands of gallons) has the pdf
If the stockpile consists of two thousand gallons at the beginning of each week (and nothing extra is received during the week), what is the probability of not being able to meet the demand during a given week?
Answer to relevant QuestionsLet f(x) = 1/2, −1 ≤ x ≤ 1, be the pdf of X. Graph the pdf and cdf, and record the mean and variance of X. Use the moment-generating function of a gamma distribution to show that E(X) = αθ and Var(X) = αθ2 Let the random variable X be equal to the number of days that it takes a high-risk driver to have an accident. Assume that X has an exponential distribution. If P(X < 50) = 0.25, compute P(X > 100 | X > 50). If Z is N(0, 1), find (a) P(0 ≤ Z ≤ 0.87). (b) P(−2.64 ≤ Z ≤ 0). (c) P(−2.13 ≤ Z ≤ −0.56). (d) P(|Z| > 1.39). (e) P(Z < −1.62). (f) P(|Z| > 1). (g) P(|Z| > 2). (h) P(|Z| > 3). Suppose that the length W of a man’s life does follow the Gompertz distribution with λ(w) = a(1.1)w = ae(ln 1.1)w, P(63 < W < 64) = 0.01. Determine the constant a and P(W ≤ 71 | 70 < W).
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