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
\mu=6 and variance \sigma^{2}=12.
(a) Find the values of \alpha and \beta.
(b) Find the probability that on any given day the daily
power consumption will exceed 12 million kilowatthours.

a)

b) 0.0620

Step-by-step explanation:

We are given the following in the question:

Population mean, = 6

Variance, = 12

a) Value of

We know that

Dividing the two equations, we get,

b) probability that on any given day the daily  power consumption will exceed 12 million kilowatt hours.

We can write the probability density function as:

We have to evaluate:

0.0620 is the required probability that on any given day the daily  power consumption will exceed 12 million kilowatt hours.

this is answer of 144 cubic meters