NAME: Solutions BU ID: Problem 4 Suppose that we flip a coin 10 times and roll...

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NAME: Solutions BU ID: Problem 4 Suppose that we flip a coin 10 times and roll a die 10 times. Let X be a random variable that indicates the number of heads for the coin flips, let Y be a random variable that counts. the number of tails for the coin flips, and let Z be a random variable that counts the number of 1s on the die. (A) Determine E[X], E[Y], and E[Z]. (B) Use (A) to compute E[X+Y] and E[Y+Z]. (C) Determine Var[X] and Var[Y]. (D) What can you say about Var[X+Y]? NAME: Solutions BU ID: Problem 4 Suppose that we flip a coin 10 times and roll a die 10 times. Let X be a random variable that indicates the number of heads for the coin flips, let Y be a random variable that counts. the number of tails for the coin flips, and let Z be a random variable that counts the number of 1s on the die. (A) Determine E[X], E[Y], and E[Z]. (B) Use (A) to compute E[X+Y] and E[Y+Z]. (C) Determine Var[X] and Var[Y]. (D) What can you say about Var[X+Y]?