Question

Suppose that, on average, it is known that a certain TV part lasts α years. The length of time the TV part lasts is exponentially distributed. A study shows that 80% of these parts last longer than 2 years. (a) What is the probability that one of these parts will last at least 3 years? (b) 90% of these parts will last at least ____ years. (c) What is the probability that one of these parts will last between one and two years? (d) What is the probability that one of these parts lasts longer than three years given that it has lasted two years?

Answer 1

a)

Let X denote the life of a TV (in years). Then

Now,

So,

Required probability =

b)

We want to find 'x' such that P(X>x) = 0.90

i.e. 0.94434 years

c)

Required probability =

d)

Required probability =