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 1 and 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 pro...

If the annual proportion of new restaurants that fail in a given city may be looked upon

Question:

If the annual proportion of new restaurants that fail in a given city may be looked upon as a random variable having a beta with α = 1 and β = 4, find
(a) The mean of this 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.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...