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

### Question Description

I don’t understand this Statistics question and need help to study.

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 Y 0 1 2 3 0 k 0.02 0.01 0.04 1 0.03 0.04 0.04 0.05 2 0.02 0.01 0.05 0.66

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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

iainharlow (1041)
Purdue University
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