A system consists of two components whose lifetimes (in years) X1, X2 are inde-pendent and identically distributed with pdf f(x) = 0.5e−0.5x, x >0. (a) Show that the mean of X is 2 and use this to find E(X2−2X1). (b) ComputeP(X2= 2X1) andP(X2>2X1). (c) ComputeCov(X1, X2−2X1). You may use the fact that Var(X1) = 4.
A system consists of two components whose lifetimes (in years) X1, X2 are inde-pendent and identically distributed with pdf f(x) = 0.5e−0.5x, x >0. (a) Show that the mean of X is 2 and use this to find E(X2−2X1). (b) ComputeP(X2= 2X1) andP(X2>2X1). (c) ComputeCov(X1, X2−2X1). You may use the fact that Var(X1) = 4.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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A system consists of two components whose lifetimes (in years) X1, X2 are inde-pendent and identically distributed with
f(x) = 0.5e−0.5x, x >0.
(a) Show that the mean of X is 2 and use this to find E(X2−2X1).
(b) ComputeP(X2= 2X1) andP(X2>2X1).
(c) ComputeCov(X1, X2−2X1). You may use the fact that Var(X1) = 4.
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