The lifetime, in years, of some electronic component is a continuous random variable with the density f(x) =   k x4 for x ≥ 1 0 for x < 1. Find k, the cumulative distribution function, and the probability for the lifetime to exceed 2 years.

I suppose the density is supposed to be

(since diverges as , and 0 is conveniently left out of the domain)

For this to be a proper density function, it must be positive (it is) and its integral over the support must evaluate to 1. We have

which means .

The distribution function is obtained by integrating the density:

The probability that the component exceeds 2 years in its lifetime is

00

step-by-step explanation:

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values