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91. Let X be a RV with support set {0, 1, 2}, p(1) = 0.3, and...

91. Let X be a RV with support set {0, 1, 2}, p(1) = 0.3, and p(2) = 0.5. Calculate E[X]. Let X be a discrete RV. Define the expected value E[X] of X. Is E[X] constant or random? Why?

92. Suppose X is a RV with support {−1,0,1} where p(−1) = q and p(1) = p. What relationship must hold between p and q to ensure that E[X] = 0?

93. Let X be a discrete RV and a, b be constants. Prove that E[a + bX] = a + bE[X].

94. Suppose that E[X] = 8 and Y = 3 + X/2. Calculate E[Y].

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