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I understand Mean (Expected Value) and Variance of Random variables as outlined on this page. I can't seem to apply those concepts to this problem, however.

Say there's a class of 50 people answering a question. There is a 60% chance that any given student knows the answer. Let $X$ be the number of students who get the correct answer.

My general sense for Expected Value in this case is just $0.6 \cdot 50=30$. But I don't think that's correct.

I don't even know how to approach Variance in this case. Each student is equally likely to get the correct answer and I keep getting large numbers which make no sense:

$$\sum_{i=0}^{50}\left(\left(i-30\right)^2\cdot0.6\right)\approx7395$$

That is obviously incorrect... can anybody offer any pointers?

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    Let $X_i = 1$ if the $i$-th student gets the correct answer and $X_i = 0$ otherwise. What is the mean of $X_i$? What is the variance of $X_i$? Do these answers depend on $i$? Have you been taught that the mean of $X_1 + X_2 + \cdots + X_{50}$ is just the sum of the means? What about the variance of $X_1 + X_2 + \cdots + X_{50}$?2011-12-06

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