An intercom system master station provides music to six hospital rooms The probability that any one room will be switched on and draw power at any time is 0.4. When on, a room draws 0.5 W. Find and plot the density and distribution functions for the random variable "power delivered by the master station". If the master-station amplifier a overloaded when more than 2 W is demanded, what is its probability of overload?
Explanation / Answer
probability to switch on is p=.4 probability to swith off is q=1-p=0.6 (a) density function f(x)=sumation (k->0 to n) (nCk)* p^k * q^(n-k)*impluse(x-k) here n=6 at plot is impluses with amplitude x amplitude 0 0.05 1 0.18 2 0.31 3 0.27 4 0.14 5 0.04 6 0 for PDF F(x=n)=sumation (k->0 to n) (nCk)* p^k * q^(n-k)*U(x-k) n=6 the plot is stair case with amplitudes at x= x amplitude 0 0.05 1 0.23 2 0.54 3 0.81 4 0.95 5 0.99 6 0.1 (b) to get overload P=1-P(X