The initial value of an appliance is $700 and its dollar value in the future is given by
Where t is time in years. Thus, after the first three years, the appliance is worth nothing as far as the warranty is concerned. If it fails in the first three years, the warranty pays v(t). Compute the expected value of the payment on the warranty if T has an exponential distribution with mean 5.
Answer to relevant QuestionsLet X have a logistic distribution with pdf Show that Has a U(0, 1) distribution. If X is N(μ, σ2), show that the distribution of Y = aX + b is N(aμ + b, a2σ2), a ≠ 0. Let the distribution of X be N(μ, σ2). Show that the points of inflection of the graph of the pdf of X occur at x = μ ± σ. A frequent force of mortality used in actuarial science is λ(w) = aebw + c. Find the cdf and pdf associated with this Makeham’s law. Let X and Y have a trinomial distribution with parameters n = 3, pX = 1/6, and pY = 1/2. Find (a) E(X). (b) E(Y). (c) Var(X). (d) Var(Y). (e) Cov(X, Y). (f) ρ.
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