1) Let X and Y be independent random variables with moment generator functions given by MX...

1) Let X and Y be independent random variables with moment generator functions given by MX (t) = (0, 4e t + 0, 6) ^8 and MY (t) = (0, 4e t + 0, 6) ^4 .

a) Determine a moment generating function of Z = 3Y + 2.

b) Determine a moment generating function of W = X + Y. What is the distribution of W?

c) Find E [W] and Var [W].

2) The annual profits that companies A and B earn follow a normal distribution bivariate. Company A's annual profit averages 2000 and standard deviation 1000. Company B has an annual profit with an average of 3000 and a standard deviation of 500. The correlation coefficient between those annual profits is 0.80. Calculate the probability that company B’s annual profit will be lower than 3900, considering that the annual profit of company A is 2300.

Expert Solution

orchestra answered 2 years ago

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