Reference no: EM132483705

Question

A particular coin is biased. Each time it is flipped, the probability of getting a head is P(H)=0.8. Each flip is independent of the other flips.

a) In a game, the coin is flipped 11 times. Let X be the total number of times the coin shows a head out of 11 flips. Calculate the following probabilities:

i) What is the probability of getting exactly 5 heads?

Correct Answer: 0.009689 .

ii) What is the probability of getting at most 5 heads? 

Correct Answer: 0.011654

iii) What is the probability of getting more than 5 heads? 

Correct Answer: 1-0.11654

b) We now want to compute the expected value and variance of X.

i) Compute the expected value. 

μX =  

Correct Answer: 8.8

ii) Compute the variance. σ2X =  

Correct Answer: 1.76

c) When you play the game, you need to pay 9 dollars to enter the game, then you toss the coin 11 times. You win 2 dollars per head. Let Y be the net amount you win when you play this game (once).

i) How much money can you expect to win per game (net amount) if you play that game a very large number of times?

Correct Answer: 8.6

ii) In order to assess how risky the game is, calculate the variance of Y.

Correct Answer: 7.04 ( I can't work this question out, please help, I want to understand it)