Consider a random experiment of tossing a biased coin three times. We assume that the tosses...

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Consider a random experiment of tossing a biased coin three times. We assume that the tosses are indepen- dent of each other and the probability of a head is 0.3. Let X be the random variable whose value represents the number of heads obtained. (a) (5 pts) List the possible outcomes of three coin tosses. What are the probabilities Pr[X = 0], Pr[X = 1], Pr[X = 2], Pr[X = = 3]? (b) (10 pts) Compute E[X] using the definition of expected value (i.e., without the use of indicator random variables). Show your work. (c) (10 pts) Let X; be an indicator random variable, whose value is 1 if the i-th toss resulted in heads. Define X in terms of Xi's and compute E[X] using this expression. Show your work. Consider a random experiment of tossing a biased coin three times. We assume that the tosses are indepen- dent of each other and the probability of a head is 0.3. Let X be the random variable whose value represents the number of heads obtained. (a) (5 pts) List the possible outcomes of three coin tosses. What are the probabilities Pr[X = 0], Pr[X = 1], Pr[X = 2], Pr[X = = 3]? (b) (10 pts) Compute E[X] using the definition of expected value (i.e., without the use of indicator random variables). Show your work. (c) (10 pts) Let X; be an indicator random variable, whose value is 1 if the i-th toss resulted in heads. Define X in terms of Xi's and compute E[X] using this expression. Show your work.