X is defined as X = E!, where I; is a random variable, which takes the values of 0 and 1 according to the toss of a fair coin in the jth trial. a) Find the mean and variance of X. b) Find the probability that X is within one standard deviation of the mean. c) Assume that another random variable is defined as Y = I;, where I, is defined as the same as before. Calculate

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2. X is defined as X = E!, where I; is a random variable, which takes the values of 0 and 1 according to the toss of a
fair coin in the jth trial.
a) Find the mean and variance of X.
b) Find the probability that X is within one standard deviation of the mean.
c) Assume that another random variable is defined as Y = E I;, where I, is defined as the same as before. Calculate
the correlation coefficient of X and Y.
%3D
Transcribed Image Text:2. X is defined as X = E!, where I; is a random variable, which takes the values of 0 and 1 according to the toss of a fair coin in the jth trial. a) Find the mean and variance of X. b) Find the probability that X is within one standard deviation of the mean. c) Assume that another random variable is defined as Y = E I;, where I, is defined as the same as before. Calculate the correlation coefficient of X and Y. %3D
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