Reference no: EM131369632
Exercises
1.1. Express the following expression in summation notation and verify your answer:
x1y4 + x6y6 +x11y8 + x16y10
1.2. Write out and simplify the following expressions:
(a) i=1Σ3 (3a - 4i)
(b) [5i=1Σ4 (19 + 11xi) - 30i=1Σ4yi] / [i=1Σ4 (33xi + 57) - i=1Σ418yi]
(Hint: Combine all terms in the numerator under one summation sign, and do the same for the denominator. Compare the two obtained expressions and find what should be factored out there for cancellation.)
(c) i=1Σ3 j=1Σ4(3xi - 4yj)
1.3. Let z be a standard normal variable. Find:
P(z>-.93)
1.4. Suppose a mutual fund has an annual rate of return that is approximately normally distributed with mean 6% and variance 49 (the variance is a square measure, not a percent).
Find the probability that the annual return will be between 4% and 10%.
1.5. The below table gives daily deliveries of X parcels to a business office, from a 0 minimum to a 15 maximum, and the number of days each delivery happened during a 100-workday period, i.e., 0 parcels delivered 2 days, 2 parcels 5 days, etc.
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Parcels per day, X
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0
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2
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3
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5
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8
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10
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15
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Number of days
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2
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5
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10
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20
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25
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24
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14
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(a) Give the probability density function of X in the table:
(b) Compute the expected value of X. Explain its meaning.
(c) Compute the variance and standard deviation of X.
(d) Using answers in (b) and (c), give the expected value and variance of Y=4+5X.
1.6. The following table gives 60 observations on three mutual funds, Y, with the average rates of return X of 10% and 25%.
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Y
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1
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2
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3
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X
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10
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6
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3
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15
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25
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12
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21
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3
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(a) Give the marginal probability functions of X and Y in the following table:
(b) Compute Cov(X,Y).
(c) Find the conditional probability density function of Y given that X = 10.
(d) Check if X and Y are statistically independent. Then explain the meaning in economic terms.
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: Compute the expected value of X. Explain its meaning. Compute the variance and standard deviation of X. Using answers in (b) and (c), give the expected value and variance of Y=4+5X.
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