# Question: If the probability is f x that a product fails the

If the probability is f(x) that a product fails the xth time it is being used, that is, on the xth trial, then its failure rate at the xth trial is the probability that it will fail on the xth trial given that it has not failed on the first x – 1 trials; symbolically, it is given by Z(x) = f (x) / 1 – F(x– 1) where F(x) is the value of the corresponding distribution function at x. Show that if X is a geometric random variable, its failure rate is constant and equal to θ.

**View Solution:**## Answer to relevant Questions

A variation of the binomial distribution arises when the n trials are all independent, but the probability of a success on the ith trial is θi, and these probabilities are not all equal. If X is the number of successes ...We did not study the Bernoulli distribution in any detail in Section 5.3, because it can be looked upon as a binomial distribution with n = 1. Show that for the Bernoulli distribution, µ'r = θ for r = 1, 2, 3, . . ., ...Differentiating with respect to λ the expressions on both sides of the equation Derive the following recursion formula for the moments about the mean of the Poisson distribution: For r = 1, 2, 3, . . .. Also, use this ...Suppose that the probability is 0.63 that a car stolen in a certain Western city will be recovered. Use the computer printout of Figure 5.1 to find the probability that at least 8 of 10 cars stolen in this city will be ...Use Chebyshev’s theorem and Theorem 5.3 to verify that the probability is at least 35 36 that (a) In 900 flips of a balanced coin the proportion of heads will be between 0.40 and 0.60; (b) In 10,000 flips of a balanced ...Post your question