5. A continuous life distribution is said to be an IFR (increasing failure rate)

distribution if its failure rate function λ(t ) is nondecreasing in t .

(a) Show that the gamma distribution with density

is IFR.

(b) Show, more generally, that the gamma distribution with parameters α, λ is IFR whenever α ≥ 1.
Hint: Write

Transcribed Image Text:

f(t) = 2 teh, t>0