Solutions to Practice Exam 2
Part I:
1. True.
2. True.
3. False. For cont. r.v., f(x) is not a probability!
4. True.
5. False. x=0,1,2…n. (It is important to correctly notify the range of x!!!)
6. False. should be 1/(ba)
7. False. P(X≤a)=F(a). (For cont. r.v. we have P(X≤a)=P(X<a), but not for discrete r.v. )
8. False. based on Central Limit Theorem for large sample, not X
i
.
9. True.
10. True.
Part II:
1.
So the probability that X lies within one standard deviation of its mean is around 68%.
In order to solve for 2 and 3 standard deviations, solve the following:
and .
2.
Y is a continuous random variable.
To find k, we take the integral over all values for which Y is defined, and set it equal to 1.
(Technically, k = 4 or 4, but if k=4, then we would be summing over a negative function and our
probabilities would be negative, so we choose positive 4.)
The mean and variance can be found by solving the following inequalities:
=8/9
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 Spring '08
 Mendell
 Normal Distribution, Probability distribution, Probability theory, maximum error, maximum error formula

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