Problem 4 (Independence?). A fair coin is tossed 10 times. Let X denote the random variable representing the number of h

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Problem 4 Independence A Fair Coin Is Tossed 10 Times Let X Denote The Random Variable Representing The Number Of H 1 (198.12 KiB) Viewed 72 times

Problem 4 (Independence?). A fair coin is tossed 10 times. Let X denote the random variable representing the number of heads and Y denote the number of tails. (4.1) Easy. Compute the variance of X. (4.2) Easy. Note that Y 10 – X. Use this formula to compute the variance of Y. (4.3) Moderate. Compute the variance of X +Y. (Hint: Recall that Y = 10 – X.] (4.4) Challenging. Use (4.3) to compute the correlation between X and Y. Are X and Y indepen- dent random variables? (4.5) Challenging. Compute the variance of 2X – Y.