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midterm2

# midterm2 - 2(1(7 The joint mass function for random...

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2 (1) (7) The joint mass function for random variables X and Y is in the following table: p(x,y) X= -5 X=5 X=10 Y=10 0 . 05 0 . 15 0 . 2 Y=20 0 . 15 0 . 10 0 . 35 (a) (1) Compute the marginal mass functions p X ( x ) and p Y ( y ) (b) (2) Compute E ( X ) and V ( X ) (c) (2) Compute E ( Y ) and V ( Y ) (d) (1) Compute Cov ( X, Y ) (e) (1) Compute Corr ( X, Y )

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3 (2) (6) Assume the temperature in July across the country follow a Normal distribution with mean 80 o F and variance 25. (a) (1) What’s the probability a randomly selected county’s July temperature is between 85 o F and 100 o F? (b) (1) What’s the probability a randomly selected county’s July temperature is between 70 o F and 90 o F? (c) (1.5) If a researcher plans to randomly sample 16 counties, what’s the probability that average July temperature of the 16 counties is between 76 . 5 o F and 81 . 5 o F? (d) (1.5) Later 16 counties have been randomly selected and their July temperatures measured. The average temperature is 78 . 6 o F. Assume the researcher does not know the actual population mean, but he knows variance is 25. Construct a 99%
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midterm2 - 2(1(7 The joint mass function for random...

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