Question

Assume the life of a roller bearing follows a Weibull distribution with parameters β=2 and δ=7,500 hours.

1. Determine the probability that the bearing will last at least 8000 hours.
2. Determine the expect value and the variance.

Answer 1

Answer:-

Given That:-

The life time of a roller bearing follows a Weibull distribution with parameters β=2 and δ=7500 hours

Let

The probability density function

The distribution function is

mean of

Variance of

Now ,here wed have

a)Determine the probability that the bearing will last for at least 8000 hours.?

Probability that the beaing will last 8000 hours is

  

  

b)Determine the mean time to failure and the variance.?

mean of

  

  

Variance of