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**1. Homework Statement**

Suppose that, on average, 70% of graduating students want 2 guest tickets for a graduation ceremony, 20% want 1 guest ticket and the remaining10% don't want any guest tickets.

(a) Let X be the number of tickets required by a randomly chosen student. Find the mean and variance of X.

(b) If 500 guest tickets are available for a ceremony at which 300 students are graduating, what is the probability that there will not be enough tickets to satisfy demand?

**2. Homework Equations**

Variance = E(X

^{2}) - E

^{2}(X)

**3. The Attempt at a Solution**

I've got the mean to be ((0.7*2) + (0.2*1) + (0.1*0))/3 = 0.53and the variance to be ((0.7

^{2}*2) + (0.2

^{2}*1) + (0.1

^{2}*0))/3 - 0.53

^{2}= 0.7391 but this seems wrong because the variance is then bigger than the mean?!?!?!