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The joint probability distribution

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The joint probability distribution on the returns of two securities X and Y is shown in the table below.

Y 7 10 14
8 0.12 0.03 0.3
9 0.15 0.09 0.06
10 0.05 0.18 0.02

a. Calculate the expected return for each security
b. Calculate the variance and standard deviation for each security
c. Suppose an investor would like to constitute a portfolio of 40 % of X and 60 % of Y, what will be the expected return and the risk associated to this portfolio?

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The joint probability distribution is determined.

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Normal Distribution and Joint Probability Distribution

54. Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65 and standard deviation .85 (suggested in "Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants," Water Research, 1984: 1169?1174).

a. If a random sample of 25 specimens is selected, what is the probability what is the probability that the sample average sediment density is at most 3.00? Between 2.65 and 3.00?

b. How large a sample size would be required to ensure the the first probability in part (a) is at least .99?

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