If X is N(μ, σ2), show that the distribution of Y = aX + b is N(aμ + b, a2σ2), a ≠ 0.
Answer to relevant QuestionsIf the moment-generating function of X is given by M(t) = e500t+5000t2, find P[27, 060 ≤ (X − 500)2 ≤ 50, 240]. If the moment-generating function of X is M(t) = exp(166t + 200t2), find (a) The mean of X. (b) The variance of X. (c) P(170 < X < 200). (d) P(148 ≤ X ≤ 172). 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). In a smoking survey among boys between the ages of 12 and 17, 78% prefer to date nonsmokers, 1% prefer to date smokers, and 21% don’t care. Suppose seven such boys are selected randomly. Let X equal the number who prefer ...An insurance company sells both homeowners’ insurance and automobile deductible insurance. Let X be the deductible on the homeowners’ insurance and Y the deductible on automobile insurance. Among those who take both ...
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