Given the following valid probability distribution of a discrete random variable X with unknown entries, X 0 1 X3 3 4 p(x) p₁ 0.1321 0.3774 0.1509 0.0377 Choose one from the following which is always correct. O c. 3 must be a real number between 1 and 3 and p₁ must be 0.3019. O b. 3 can be any real number other than 0, 1, 3, 4, and p₁ must be 0.3019. e. 3 can be any real number and p₁ must be 0.3019. a. 3 must be 2 and p₁ must be 0.3019. O d. 03 can be any real number other than 0, 1, 3, 4, and p₁ can be any nonnegative real number that is smaller that 1.

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

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Let X be a random variable with the following PMF: X = k k=-5 k=-2 k=0 k=2 k=5 P(X=k) 0.3 0.05 0.05 0.2 0.4 What is the probability that X is a negative number. Group of answer choices 0.6 0.4 0.35 1