An insurance company insures a large number of homes The ins

An insurance company insures a large number of homes. The insured value, X, of a randomly selected home is assumed to follow a distribution with density function f(x)=4x^(-5) , for x>1. Given that a randomly selected home is insured for at least 2, what is the probability that it is insured for less than 4?

Solution

Here,

f(x) = 4x^-5

Note that

P(x<4|x>=2) = P(2<=x<4) / P(x>=2)

As

P(2<=x<4) = Integral [4x^-5 dx] | (2,4) = -x^-4 | (2,4) = 0.05859375

P(x>=2) = -x^-4 | (2,oo) = 0.0625

Thus,

P(x<4|x>=2) = P(2<=x<4) / P(x>=2) = 0.9375 [answer]