Suppose X is an exponential random variable with mean parameter equal to 1. 1 Derive the distribution of Y = aX1/8, for a > 0, 3>0. Specify its density function. The distribution of Y is called a Weibull and we can write Y~Weibull(a. 3) where a is obviously a scale parameter. 2 Derive the mean and variance of Y. Assume that the future lifetime (in years) of an iPhone follows a Weibull distribution with mean 8 and variance 320. Calculate the probability that an iPhone fails within the first 5 years of use.
Suppose X is an exponential random variable with mean parameter equal to 1. 1 Derive the distribution of Y = aX1/8, for a > 0, 3>0. Specify its density function. The distribution of Y is called a Weibull and we can write Y~Weibull(a. 3) where a is obviously a scale parameter. 2 Derive the mean and variance of Y. Assume that the future lifetime (in years) of an iPhone follows a Weibull distribution with mean 8 and variance 320. Calculate the probability that an iPhone fails within the first 5 years of use.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 4E
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