MM_4_4_problems_fall11

# MM_4_4_problems_fall11 - = \$200 and the standard deviation...

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Moore and McCabe 4.4 Problems Round all of your final answers to four decimal places if necessary. #1) Mary has invested 20% of her funds in T-bills and 80% of her funds in stocks. If X is the annual return on T-bills and Y the annual return on stocks, the portfolio rate of return is: R = 0.2 X + 0.8 Y The returns X and Y are random variables because they vary from year to year: X = return on T-bills: μ X = 5 σ X = 3 Y = return of stocks: μ Y = 10 σ Y = 8 correlation between X and Y : ρ XY = -0.1 What is μ R ? What is σ R ? R = (0.2 X ) + (0.8 Y ) R = F + G (Note that ρ FG = ρ XY . F is a linear transformation of X . G is a linear transformation of Y . Linear transformations do not change the correlation. Also, recall that σ 2 a + bX = b 2 σ 2 X .)

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2. An insurance company sees that in the entire population of homeowners, the mean loss from fire is μ
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Unformatted text preview: = \$200 and the standard deviation of the loss is = \$300. a) What are the mean and standard deviation of the total loss for 5 policies? (Losses on separate policies are independent.) b) What are the mean and standard deviation of the average loss for 5 policies? 3. An estimator, y_estimator1 , is used to estimate the population mean of Y ( Y ). Suppose Y = 100 and Y = 20. Suppose an SRS of n =10 is drawn, and y_estimator1 is a weighted average in which the observations are alternatively weighted by 1/2 and 3/2: y_estimator1 = (1/10)[(1/2) Y 1 + (3/2) Y 2 + (1/2) Y 3 + (3/2) Y 4 ++(1/2) Y 9 + (3/2) Y 10 ] What is the standard deviation of y_estimator1 (rounded to four decimal places )?...
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## This note was uploaded on 02/22/2012 for the course PAM 2100 taught by Professor Abdus,s. during the Fall '08 term at Cornell University (Engineering School).

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MM_4_4_problems_fall11 - = \$200 and the standard deviation...

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