QUESTION 7Which of the following is not a characteristic of the chi-square distribution? Select all correct answers.

The mean of the chi-square distribution is located to the left of the peak.

The chi-square curve is nonsymmetrical.

The 2 curve approaches, but never touches, the positive horizontal axis.

As the degrees of freedom increases, the chi-square curves look more and more like a normal curve

QUESTION 7 Which of the following is not a characteristic of the chi-square distribution? Select all correct answers.

15 15 Short-term decision making differs from long-term decision making because: Short-term decision making assumes that variable costs are fixed. Short-term decision making assumes selling prices are fixed. Short-term decision making assumes capacity is fixed. Short-term decision making assumes the accounting data is fixed. 12 7 16244 SOME SPECIAL DISTRIBUTIONS It is easy to show (Problem 2) that cov(X. Y) = a/x, so that var(2) = 2[1 + (a/x)] If Z is normal, its MGF must be (12) Next we compute the MGF of Z directly from the joint PDF (10). We have - + +12F() - 112F()- 1If()f()dxdy = +a "[2F() - 11/()dx Now "(2F() - 1/()dx = -2 "[1 - F(x)/(x)dx + 'n exp -s(x2 + (u + x)? - zx] expl-87 /2 + (v - 1)2/4] expl-[x + (# - 0)/217) -dx du du (13) where Z, is an A(0. 1) RV. It follows that (14) 1+a(1-28/21- #21)"1. Approximate the function f(x)= xe for values of x near 0 using the first three non- zero terms of its Taylor polynomial