# Question: A certain machine has a life X that has an

A certain machine has a life X that has an exponential distribution with mean 10. The warranty is such that $m is returned if the machine fails in the first year, (0.5)m of the price is returned for a failure during the second year, and nothing is returned after that. If the machine cost $2500, find m so that the expected payment is $200.

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The time X to failure of a machine has pdf Compute P(X > 5 | X > 4). Find the mean and variance of X if the cdf of X is Let X and Y have a trinomial distribution with parameters n = 3, pX = 1/6, and pY = 1/2. Find (a) E(X). (b) E(Y). (c) Var(X). (d) Var(Y). (e) Cov(X, Y). (f) ρ. Let T1 and T2 be random times for a company to complete two steps in a certain process. Say T1 and T2 are measured in days and they have the joint pdf that is uniform over the space 1 < T1 < 10, 2 < T2 < 6, T1 + 2T2 < 14. ...Using the background of Example 4.4-4, calculate the means and variances of X and Y.Post your question