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?

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  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
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