Call that random variable a for amount of payoff a find the

Reference no: EM13621442

Suppose we were to play a game with the following rules. We pay 8 dollars to play the game. We then flip a (possibly biased, probability of heads p) coin 21 times. Our payoff is equal to three dollars plus an amount of dollars equal to half the number of heads obtained. Since we don't know how many heads will result, the payoff is a random variable. Call that random variable A (for amount of payoff). a) Find the moment generating function, M_X(t), of the random variable X. b) Differentiate to obtain M_X(t) to obtain E(X). c) Use the result of part b to find the expected winnings from playing this game. What value of p (if any) makes this a fair game?

Reference no: EM13621442

Questions Cloud

As the population ages there is increasing concern about : as the population ages there is increasing concern about the accident-related injuries to the elderly. the article age

It is desired that the true standard deviation of the : it is desired that the true standard deviation of the softening point of a certain type of petroleum pitch be at most

Test the claim that the population of kindergarden students : test the claim that the population of kindergarden students has a mean grade point average of 2.25 versus a mean grade

The manufacturer wants to check that the mean length of : suppose bolts are being manufactured using a process so that it is known that the length of the bolts follows a normal

Call that random variable a for amount of payoff a find the : suppose we were to play a game with the following rules. we pay 8 dollars to play the game. we then flip a possibly

A random sample of 100 voters in a community produced 59 : a random sample of 100 voters in a community produced 59 voters in favor of candidate a. the observed value of the test

Write down the equation of the least squares line and use : data were collected on gpa and number of faceook friends for students in a small statistics class. some summary

An airline has an advertisement that states our passengers : an airline has an advertisement that states ...our passengers always receive their bags within 20 minutes after the

Describe in words and statistical terms the relationship : a survey was carried out to find the salaries for technicians working in maintenance at atlanta international airport.

User Account

All Pages