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M1 practice questions w09

M1 practice questions w09 - MIDTERM 1 PRACTICE WINTER 2009...

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MIDTERM 1 PRACTICE WINTER 2009 PSTAT 5E Problem 1 Here are 8 data points listed. 96 6 9 1 4 3 11 84 a) Find the mean, median, and mode for the data. b) Explain why the median is different from the mean for this set of data. c) Find the variance and standard deviation for this set of data that fall less of the median.
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Problem 2 Circle the T for “true” and the F for “false”. T F If events A and B are independent, then P(AUB) = P(A) + P(B) T F The average of five students’ heights is an example of a continuous variable. T F If two events A and B are mutually exclusive, then they must be independent. T F If two events A and B are independent, then they must be mutually exclusive. T F If a z-score ‘Z’ value is calculated to be 0.25, and we know that the mean is 44 and the x-value ‘X’ is found to be 46, then the standard deviation of x is 8. Problem 3 a) Suppose that X and Y are random variables, and that we have the following information: For this problem, consider only the population case. E[X] = 5 E[Y] = 3 Var(X) = 64 SD(Y) = 12 pXY = 0.5 With this given information, determine the Cov(X,Y). b) Now, if X and Y are both binomial random variables, then, using the same information above, except that the Var(X) and SD(Y) are unknown here, but that a sample size of n=10 is used for X and n=5 is used for Y, determine the Cov(X,Y) for these binomial random variables. (hint: remember the formulas!)
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Problem 4 Four fair coins are flipped, one after another. a) Define the sample space for this set of events. b) Find the probability that all 4 of the coins landed on the same value. c) If we know that the first coin landed ‘heads’ for sure, but we do not know which of the next 3 did or did not, find the probability that exactly 3 heads were made.
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