Let x unif[0; 1]. parts (a) and (b) below ask you to nd the nth moment of x in two di erent ways. (a) use the formula e(xn) = r 1 0 xn dx. (b) compute the moment generating function mx(t) (or use the result of exercise 5.3). find the taylor series expansion of mx(t) and identify the coecients. hint. mx(t) will be written in terms of et. substitute the taylor series for et into the formula and simplify the expression.

Aresearch study is studying the effects of a new drug for osteoporosis alzheimer's disease (ad) for women above the age of 65 years. a group of individuals with osteoporosis is randomized into two groups. one group is treated conventionally, and the second group is treated with the new medication. assessments are made at 3, 6, 12, 36, and 48 months. the conventionally treated group is assessed for ad using a serum blood test, and the treatment group is assessed for ad using a pet radiotracer that binds to beta-amyloid plaques. in comparing these 2 trial arms, the authors of the study may encounter which type of bias? a. selection bias on the risk of developing b. measurement bias c. confounding bias d. recall bias e. lead-time bias