(Answered) Let x denote the number of heads obtained when a fair coin

Statistics

Let X denote the number of heads obtained when a fair coin is tossed four times.

(a) What is E[X] and Var X?

(b) Perform the experiment of tossing a fair coin four times and recording the number of heads obtained 10 times. You thus obtain a random sample of size 10 from a binomial distribution with n = 4 and p = 1.

(c) Based on your 10 observations, estimate the mean and variance of X. Compare your answers to those of your classmates. Do the observed values of X fluctuate about the theoretical mean of 2? Do the observed values of S2 fluctuate about the theoretical variance of 1?

(d) Average the values of X that you have available. Is the average value close to 2? Average the values of S2 that you have available. Is the average value of S2 close to 1?

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