STAB22H3 Lecture : Statistics Lecture Note

Find the least integer n such that f (x) is O(xn ) for each of these functions.
(a) f (x) = 2x2 + x3 log x
(b) f (x) = 3x5 + (log x)4
(c) f (x) = (x4 + x2 + 1)/(x4 + 1)
(d) f (x) = (x3 + 5 log x)/(x4 + 1)

Consider a binomial experiment with n=20 and p=0.70.

• Compute f(12).
• Compute f(16).
• Compute P(x >= 16).
• Compute P(x <= 15).
• Compute E(X).
• Compute Var(X).

8. Let f(x) = z^ \n(x2 + 7). Then f'(2) is (a) 32 ln(11) + 4/11, (b) 32 In(11) + 16/11, (c) 32 ln(11), (e) 32 ln(11) + 16. (d) 32 In(11) +64/11,