a) What must the value of k be for this to be a valid probability model?

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A restaurant needs a staff of 3 waiters and 2 chefs to be properly staffed. The joint probability model for the number of waiters (X) and chefs (Y) that show up on any given day is given below. 


X
Y0123
0k0.020.010.04
10.030.040.040.05
20.020.010.050.66

Oct 22nd, 2017

The entries in the model are mutually exclusive. That means, if there are 1 waiters and 2 chefs, there are not 2 waiter and 2 chefs for example!

So, that means all the probabilities together must sum to 1. So we have:

1 - 0.03 - 0.02 - 0.02 - 0.04 - 0.01 - 0.01 - 0.04 - 0.05 - 0.04 - 0.05 - 0.66 = k

k = 1-0.97

k = 0.03

Mar 8th, 2015

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