You participate in a coin-flipping game in which you win based on how many heads show...

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You participate in a coin-flipping game in which you win based on how many heads show up. In this game you flip a fair coin n times. For each time that you flip a coin you pay d dollars. If Head shows up M times you win 2M² + M dollars. What is the expected value of the net reward? • Modify the previous problem, and change the reward for flipping M heads to 2M. Find the expected value of the net reward. : For problems 3 and 4 you can use the identity -Σω Σ)- (a + b)" = E (") ambn-m %3D You participate in a coin-flipping game in which you win based on how many heads show up. In this game you flip a fair coin n times. For each time that you flip a coin you pay d dollars. If Head shows up M times you win 2M² + M dollars. What is the expected value of the net reward? • Modify the previous problem, and change the reward for flipping M heads to 2M. Find the expected value of the net reward. : For problems 3 and 4 you can use the identity -Σω Σ)- (a + b)" = E (") ambn-m %3D