4. (Portfolio Returns.) The Long-Term Capital Depreciation Group owns a port- folio that has $20,000 in a fund holding US stocks, and $30,000 in a fund hold- ing European stocks. The annual return on the US fund is (approximately) normally distributed with mean 10% and standard deviation 5%.1 The an- nual return on the European fund is (approximately) normally distributed with mean 1% and standard deviation 8%. The covariance between the two fundsâ€™ annual returns is 0.002. (a) Compute the probability distribution of the value of the Long-Term Cap- ital Depreciation Groupâ€™s portfolio after one year. (b) What is the probability that the value of their portfolio at year end is less than $50,000?
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