Suppose two independent discrete random variables X₁ and X2. Both follow a discrete distribution such that p(1) = 0.5, p(2) = 0.3, and p(3) = 0.2. Let X = X₁+X2. What is P(X) = 2)? a. 0.09 b. 0.29 c. 0.3 d. 0.6

Q P.6: On its way, a car meets 4 traffic lights, and the probability that each of them will be red is 0.5. Let X be a discrete random variable equal to the number of traffic lights that were green when the car arrived. X may take the values of 0, 1, 2, 3, 4. (Assume traffic lights are independent.) What is the probability distribution of X? The probability distribution of X is 3 4 p(x) 0.5 0.25 0.125 0.0625 0.0625 The probability of distribution of X is 3 p(x) 0.5 0.5 0.25 0.125 The probability of distribution of X is 3 4 p(x) 0.5 0.25 0.5 0.25 0.125 The probability distribution of X is 1 3 4 p(x) | 0.5 || 0.5 || 0.5 | 0.5 || 0.5 The probability of distribution of X is 3 4 p(x) || 0.0625 0.0625 0.125 0.25 0.5

Let discrete random variables X and Y have the following probability distribution: Y 1 -1 0.10 0.18 0.10 X 0.09 0.15 0.23 1 0.03 0.05 0.07 Find the E(X2 Y²) -0.91 1.18 0.91 1.0494