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  3. 1 suppose that company a and company b are in...

Question: 1 suppose that company a and company b are in...

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1. Suppose that company A and company B are in the same industry sector, and the prices of their stocks, SX per share for company A and SY per share for company B, vary from day to day randomly according to a bivariate normal distribution with parameters μΧ=50, σχ= 10, μΥ-27, σΥ= 3, ρ=0.6. ) What is the probability that on a given day the price of stock for company A (x) is below $44? That is, find P(X<44). b) Suppose that on a given day the price of stock for company B (Y) is $25. What is the probability that the price of stock for company A (X) is below $44? That is, find P(X <44 Y-25) c) Suppose that on a given day the price of stock for company A (X) is S54. What is the probability that the price of stock for company B (Y) exceeds S302 That is, find P(Y>30 X-54). d) What is the probability that 1 share of company A stock is worth more than 2 shares of company B stock? That is, find P (X>2Y). e Alex bought 5 shares of company A stock and 4 shares of company B stock What is the probability that on a given day the value of his portfolio (5 X+4 Y) exceeds $300? That is, find P(5X4Y> 300). 1. (continued) Suppose that the price of stock for company C, SW per share, also varies from day to day and (X, Y, W) jointly follow N3(H. 2) distribution with 50 H27 45 100 18 22 2 18 9 12 22 12 25 and f) What is the probability that on a given day the price of stock for company C(W) is below $47? That is, find P(W < 47) g What is the value of pyw? h) Suppose that on a given day the price of stock for company C(W) is $46. What is the probability that the price of stock for company B (Y) exceeds $30? That is, find P(Y>30 W-46) Hint, ( Y, W ) jointly follow a bivariate normal distribution. i) Alex bought 5 shares of company A stock, 4 shares of company B stock, and 2 shares of company C stock. What is the probability that on a given day the value of his portfolio (5X +4Y+2 W) exceeds $400? That is, find P (5X+4Y+2W> 400).

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