Question: 1. In a certain city, the daily consumption of electric power, in millions of kilowatt-hours, is a random variable X having a gamma distribution with

1. In a certain city, the daily consumption of electric power, in millions of kilowatt-hours, is a random variable X having a gamma distribution with mean = 6 and variance 2 = 12. (a) Find the values of and . (b) Find the probability that on any given day the daily power consumption will exceed 12 million kilowatthours.

In a biomedical research study, it was determined that the survival time, in weeks, of an animal subjected to a certain exposure of gamma radiation has a gamma distribution with = 5 and = 10. (a) What is the mean survival time of a randomly selected animal of the type used in the experiment? (b) What is the standard deviation of survival time? (c) What is the probability that an animal survives more than 30 weeks?

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