Problem 163E

Suppose that the lifetime of a component (in hours) is modeled with a Weibull distribution with β = 2 and δ = 4000. Determine the following in parts (a) and (b):

Answer

Step 1 of 3

(a)

Suppose that the lifetime of a component ( in hours) is modeled with a Weibull distribution with

We are asked to find the probability

The random variable with probability density function

is a Weibull random variable with scale parameter and shape parameter .

The cumulative distribution function of is

………(1)

We can write as,

Using equation (1), we can write,

Hence the probability is