4. [15 pts] Dede has accounts in 10 banks. Starting with $10 in his wallet and...

Transcribed Image Text:

4. [15 pts] Dede has accounts in 10 banks. Starting with $10 in his wallet and with a biased coin that shows heads with probability p, Dede visits each of the banks. In cach bank, he flips the coin. If it shows heads he removes $1 from his account in that bank and adds it to his wallet. If it shows tails he takes $1 from his wallet and puts it into his account in that bank. He does all this mutually independently for the 10 banks. Let X be the random variable that returns the amount of dollars that Dede has in his wallet after visiting the 10 banks. (a) [3 pts] Describe the probability space on which X is defined. (b) [3 pts] What is Val(X)? (c) [4 pts] Determine p such that E[X]=$15. D (d) [5 pts] Assuming that the coin is fair compute the standard deviation of X. Solution. (a) YOUR SOLUTION TO PART (a) HERE (b) YOUR SOLUTION TO PART (b) HERE (c) YOUR SOLUTION TO PART (c) HERE (d) YOUR SOLUTION TO PART (d) HERE 4. [15 pts] Dede has accounts in 10 banks. Starting with $10 in his wallet and with a biased coin that shows heads with probability p, Dede visits each of the banks. In cach bank, he flips the coin. If it shows heads he removes $1 from his account in that bank and adds it to his wallet. If it shows tails he takes $1 from his wallet and puts it into his account in that bank. He does all this mutually independently for the 10 banks. Let X be the random variable that returns the amount of dollars that Dede has in his wallet after visiting the 10 banks. (a) [3 pts] Describe the probability space on which X is defined. (b) [3 pts] What is Val(X)? (c) [4 pts] Determine p such that E[X]=$15. D (d) [5 pts] Assuming that the coin is fair compute the standard deviation of X. Solution. (a) YOUR SOLUTION TO PART (a) HERE (b) YOUR SOLUTION TO PART (b) HERE (c) YOUR SOLUTION TO PART (c) HERE (d) YOUR SOLUTION TO PART (d) HERE