Question: 43. A random variable X, which represents the weight (in ounces) of an article, has density function, a. Calculate the mean and variance of the

43. A random variable X, which represents the weight (in ounces) of an article, has density function,

z-8 for 89 f(z) = 10- for 9 < < 10 0

a. Calculate the mean and variance of the random variable X.

b. The manufacturer sells the article for a fixed price of $2.00. He guarantees to refund the purchase money to any customer who finds the weight of his article to be less than 8.25 oz. His cost of production is related to the weight of the article by the relation x/15+.35. Find the expected profit per article.

z-8 for 89 f(z) = 10- for 9 < < 10 0 otherwise

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