# let and be independent random variables representing the lifetime (in one billion years) of type a and type b stars, respectively.

let and be independent random variables representing the lifetime (in one billion years) of type a and type b stars, respectively. both variables have exponential distributions, and the mean of is 3 and the mean of is 11. what is the expected total lifetime of three type a stars and one type b star?

### 1 thought on “let and be independent random variables representing the lifetime (in one billion years) of type a and type b stars, respectively.”

1. The expected total lifetime of three type a stars and one type b star is 20.
The exponential distribution frequently addresses the elapsed time before a particular event. Consider the exponential distribution of the time (starting right now) before an earthquake happens. It is a continuous distribution that is frequently used to calculate time when an event is anticipated to take place.
Given let x and y be independent random variables representing the lifetime (in one billion years) of type a and type b stars, respectively. both variables have exponential distributions, and the mean of is 3 and the mean of is 11.
We have to determine what is the expected total lifetime of three type a stars and one type b star?
X, y are independent
Mean of x = 3 = ux
Mean of y= 11= uy
So sample of x =na=3
Sample of y = nb = 1
E[x] = na x ux
= 3 x 3
=9
E[y] = nb x uy
= 1 x 11
=11
Total life time expected = E[x] + E[y]
= 9 + 11
= 20
Therefore the expected total lifetime of three type a stars and one type b star is 20