Five intermittent loads are connected to a common power supp

Five intermittent loads are connected to a common power supply. Each load, when in operation, draws 10W. In addition, each load is in operation one-quarter of the time and operates independently of all other loads.

(a) What is the mean value of the power drawn by the loads.

(b) What is the variance of the power drawn by the loads.

(c) Suppose that the power supply can only provide 40W. What is the probability that the power supply is overloaded.

Solution

(a) Given n=5 and p=0.25

mean=n*p=5*0.25 =1.25

---------------------------------------------------------------------------------------------------------

(b)variance= n*p*(1-p)

=5*0.25*(1-0.25) =0.9375

---------------------------------------------------------------------------------------------------------

(c) The probability is 0.25^ 5=0.0009765625