(5) The failure time for a medical device, X, has a spliced distribution.

(i) f₁(x) follows the uniform distribution on (0,3).

(ii) f₂(x) follows the exponential distribution with mean 4.

a₁f₁(x), 0 <= x <= 3

(iii) f_X(x) = is continuous at x=3.

a₂f₂(x), x > 3

Find a₁, a₂, and the probability of failure in the first 5 years. (Ans a₁ = 0.42857, a₂ = 1.20971, prob of failure = 0.6534)