6. (Pory'olio value prediction intervals.) Les Izmor is an employee of Epsilon Inc, a major software rm. Since joining Epsilon nearly ten years ago, Les has set aside a portion of his income as savings for retirement. Like many employees, Les used these savings to purchase stock in Epsilon each month, and the total value of his Epsilon stock is now $1,000,000. (a) The quarterly rate of return on Epsilon stock is approximately normally distributed with mean 6.37% and standard deviation 18.08%. Determine an interval that, with probability .9, will contain the (total) value of his stock in Epsilon one quarter from now (Note: The interval should be wmmeiric, meaning that the possible outcomes above the interval have 1/2 the remaining probability, or .05, and the outcomes below the interval have the other 1/2 of the remaining probability, .05). This interval is known as a 90% prediction interval for Les' portfolio value in one quarter. For simplicity in calculating the intervals for this problem, you should assume that Les makes no additional purchases of Epsilon stock during this quarter. (b) Last summer, Les took a course on retirement planning where he learned about the value of diversication. He now wants to diversify his holdings between the Epsilon stock and the Sigma fund, a high-risk, high- return mutual fund. He knows that the quarterly rate-of-return on the Sigma flmd is approximately 10.31% with standard deviation 22.85%. In addition, the correlation between the quarterly return on Epsilon stock and the quarterly return on the Sigma fund is 0.25 1 . Suppose that Les keeps 46% of his current $1,000,000 retirement savings in Epsilon stock, and puts the remaining 54% in the Sigma fund. Find a (symmetric) 90% prediction interval for the value of this portfolio one quarter from now