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Suppose X, Y, and Z are three different random variables. Let X obey a Bernoulli Distribution. The probability mass function for X is: p(x)

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Suppose X, Y, and Z are three different random variables. Let X obey a Bernoulli Distribution. The probability mass function for X is: p(x) = { 0.7 0.3 x = c x = -c where c is a nonzero constant. Let Y obey the Standard Normal (Gaussian) Distribution, which can be written as Y ~ N(0, 1). X and Y are statistically independent (i.e. P(X|Y) = P(X)). Meanwhile, let Z = XY. Calculate the covariance of Y and Z (i.e. Cov(Y, Z)). Do values of c affect the covariance between Y and Z? [5pts]

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