Peter and mary take turns throwing one dart at the dartboard. peter hits the bullseye with probability p and mary hits the bullseye with prob- ability r. whoever hits the bullseye first wins. suppose peter throws the first dart. (a) what is the probability that mary wins? b) let x be the number of times mary throws a dart in the game. find the possible values and the probability mass function of x. check that the function you give sums to 1. is this a familiar named distribution? c) find the conditional probability p(x = kl mary wins), for all possible values k of x. is this a familiar named distribution?

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.