Question

The type of battery in Jim's laptop has a lifetime (in years) which follows a Weibull distribution with parameters α = 2 and β = 4 . The type of battery in Jim's tablet has a lifetime (in years) which follows an exponential distribution with parameter λ = 1 / 4 . Find the probability that the lifetime of his laptop battery is less than 2.2 years and that the lifetime of his tablet battery is less than 3.1 years.

Answer 1

Answer:

Given,

f(x) = (/)*(x/)^(-1)*e^(-x/)^ , x > 0

f(y) = 1/4 * e^-y/4 , y > 0

Now E(x) = , E(y) = 4

P((X < 2.2) (Y < 3.1)) = P(X < 2.2)*P(Y < 3.1)

= [1-e^(-2.2/4)^2][1-e^(-3.1/4)]

= 0.2610*0.5393

= 0.1408