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The lifetime of an electronic component has a Weibull distribution with parameters α​=0.60 and β​=2. Compute...

The lifetime of an electronic component has a Weibull distribution with parameters α​=0.60 and β​=2. Compute the probability the component fails before the expiration of a 4 year warranty.

The maximum flood​ levels, in millions of cubic feet per​ second, for a particular U.S. river have a Weibull distribution with α=5/3 and β=3/2. Find the probability that the maximum flood level for next year will exceed 0.7 million cubic feet per second.

Solutions

Expert Solution

The pdf of the Weibull distribution is given by:

And the CDF of Weibull distribution is:

(A)

Let the random variable denote the lifetime of electronic component.

follows the Weibull distribution with parameters

Therefore, the probability that the electronic component fails before the expiry of warranty period of 4 years is:

(B)

Let the random variable denote the maximum flood levels million cubic feet per second.

follows the Weibull distribution with parameters

Therefore, the probability that the maximum flood level for next year will exceed 0.7 million cubic feet per second is:

milcah answered 1 year ago
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