The life span of a particular brand of food processor is measured by a random variable X with probability density function

where x denotes the life span (in months) of a randomly selected processor.

a. Verify that f(x) is a probability density function by showing that

b. The expected value of X is given by the improper integral

which can be evaluated only by numerical methods. Estimate E(X) by applying Simpson’s rule with n = 10. Based on your result, how long would you expect a randomly chosen processor to last?

c. The actual expected value E(X) is roughly 28 (months). Discuss what (if anything) you could do to improve the result you obtained in part (b).

Transcribed Image Text:

f(x) = [ 0.002xe 0.001 lo for x ≥ 0 for x < 0