Shankar really likes playing Badminton. On a particular day at Fetzer gym he plays two games (whose outcomes are independent of each other). He has .3 probability of winning the first game and he has .9 probability of winning the second game. There are no ties and as stated above the outcomes of each game are independent of each other. Let X denote the number of games Shankar wins.
a. Calculate E[X] and E[X2].
b. Find a formula for M(t), the moment generating function for X.
c. Find a formula for M'(t) and check that M'(0) = E[X].
d. Find a forumla for M"(t) and use it to find Var[X].

Arandomized controlled trial is designed to evaluate the effect of metoprolol in patients with heart failure. while preparing for statistical analysis, the researcher reviews some common types of statistical errors. which of the following statements is true regarding a type i error in a clinical study? a. the study is not significantly powered to detect a true difference between study groups. bthe null hypothesis is true but is rejected in error. c. the null hypothesis is false but is accepted in error. d. type i error is also known as beta and is usually 0.1 or 0.2. e. type i error depends on the study's confidence interval.