An intercom system master station provides music to six hospital rooms The proba

Question

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

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