# Question: If the annual proportion of new restaurants that fail in

If the annual proportion of new restaurants that fail in a given city may be looked upon as a random variable having a beta distribution with α = 1 and β = 4, find

(a) The mean of this distribution, that is, the annual proportion of new restaurants that can be expected to fail in the given city;

(b) The probability that at least 25 percent of all new restaurants will fail in the given city in any one year.

(a) The mean of this distribution, that is, the annual proportion of new restaurants that can be expected to fail in the given city;

(b) The probability that at least 25 percent of all new restaurants will fail in the given city in any one year.

## Answer to relevant Questions

Suppose that the service life in hours of a semiconductor is a random variable having a Weibull distribution (see Exercise 6.23) with α = 0.025 and β = 0.500. (a) How long can such a semiconductor be expected to last? ...If X is a random variable having a normal distribution, what are the probabilities of getting a value (a) Within one standard deviation of the mean; (b) Within two standard deviations of the mean; (c) Within three ...A random variable has a normal distribution with σ = 10. If the probability that the random variable will take on a value less than 82.5 is 0.8212, what is the probability that it will take on a value greater than 58.3? Perform a suitable change of variable to show that the integral defining the gamma function can be written as Use the transformation technique to rework Exercise 7.2. In exercise If the probability density of X is given by And Y = X2Post your question