1. Suppose that the prices of the stocks for two companies, $X per share for company A and $Y per share for company B, vary from day to day randomly according to a bivariate normal distribution with parameters X = 78, X = 10, Y = 55, Y = 8, = 0.6.

a) What is the probability that on a given day the price of stock for company A ( X ) is below $66? That is, find P( X

b) Suppose that on a given day the price of stock for company B ( Y ) is $50. What is the probability that the price of stock for company A ( X ) is below $66? That is, find P( X

c) What is the probability that the price of stock for company B ( Y ) exceeds $60? That is, find P( Y > 60 ).

d) Suppose that on a given day the price of stock for company A ( X ) is $88. What is the probability that the price of stock for company B ( Y ) exceeds $60? That is, find P( Y > 60 | X = 88 ).

e) What is the probability that 1 share of company A stock is worth more than 1 shares of company B stock? That is, find P ( X > Y ).

f) 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 > 2 Y ).

g) Alex bought 6 shares of company A stock and 8 shares of company B stock. What is the probability that on a given day the value of his portfolio ( 6 X + 8 Y ) exceeds $1000? That is, find P ( 6 X + 8 Y > 1000 )

PLEASE ANSWER ALL PARTS

1. Suppose that the prices of the stocks for two companies, $X per share for company A and $Y per share for company B, vary from day to day randomly according to a bivariate normal distribution with parameters u x = 78, Ox= 10, uy = 55, Oy=8, p = 0.6. What is the probability that on a given day the price of stock for company A (X) is below $66? That is, find P(X 60). d) Suppose that on a given day the price of stock for company A (X) is $88. What is the probability that the price of stock for company B (Y) exceeds $60? That is, find P(Y>60 | X = 88). e) What is the probability that 1 share of company A stock is worth more than 1 shares of company B stock? That is, find P(X> Y). f) What is the probability that I share of company A stock is worth more than 2 shares of company B stock? That is, find P(X> 2 Y). Alex bought 6 shares of company A stock and 8 shares of company B stock. What is the probability that on a given day the value of his portfolio (6 X + 8 Y) exceeds $1000? That is, find P(6X + 8 Y> 1000)