Solutions_to_Practice_Exam2

# Solutions_to_Practice_Exam2 - Solutions to Practice Exam 2...

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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/(b-a) 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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Solutions_to_Practice_Exam2 - Solutions to Practice Exam 2...

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