Question

At a car wash a customer can pay through a cashier (X) or at a self service car wash machine (y). There are 2 cashiers and 2 self service machines. The joint probability mass function of x and y, P(x,y) represents the proportion of time that the payment system is working. P(x,y) is given as: P(0,0) = .1, P(0,1)=.08, P(1,02) = .02, P(1,0)=.08, P(1,1)=.2, P(1,2)=.06, P(2,0)=.06, P(2,1)=.1, P(2,2)=.3. Find the standard deviation of x.

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