(a) the length of life of a light bulb manufactured by a certain process has an exponential distribution with an unknown rate. Suppose the prior distribution for is a gamma distribution with a coefficient of variation of 0.5. (The coefficient of variation is defined as the standard deviation divided by the mean.) A random sample of light bulbs is to be tested and the lifetime of each obtained. If the coefficient of variation of the distribution of is to be reduced to 0.1, how many light bulbs need to be tested? (b) in part (a), if the coefficient of variation refers to instead of , how would your answer be changed?

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