7. Let X denote a random variable for the number of times some event occurs with a period of time. For example, X might denote the number of patients who come to a hospital's emergency room per hour between midnight and 6:00 AM. This random variable has probability mass function

where X = 0,1,2,3,.... andis the mean of X (i.e., ).

For purposes of this problem, assume that. That is, on average three patients come to a hospital's emergency room per hour between midnight and 6:00 AM.

(a) Place the values X = 0,1,2,3,....,15 in Column A in Excel. Calculate the probability of each of these X values occurring usinggiven above. Use Excel to draw the graph with X on the horizontal axis andon the vertical axis.

(b) What is the probability that 6 or more patients come to the hospital emergency room between midnight and 6:00 AM?

[Excel commands are =Poisson(x,,false) for the probability mass function and

=Poisson(x,,true) for the cumulative distribution function.]