Which of the following validates the a probability mass distribution? P(x) <1 P(x) S0 P(x) 2 0 P(x) 2 1 ΣΡ(x) -1
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- 9. Consider the formula: P(x) = x/21, x 0, 1, 2, 4. Is P(x) a probability mass function? If so, show the distribution of X in tabular form and compute the expected value of X.The continuous random variable Y has the following pdf: 1- y?, 0Joint probability distribution: 1. 4 4 5 6 fxy(x,y) 1/8 1/4 1/2 1/8 O xy or the covariance= VX) = V(Y) =Q1 Let probability distribution function of Xbe defined by х %3D 0,1, 2, 3. a P(x) = otherwise. Find the value of a. (а) (b) (c) (d) Find P(-1Consider the following discrete probability distribution:- X 2 4 6 8 10 P(X = x) 0.3 0.3 0.2 0.1 0.1 Find: P(X < 8) E[X] Variance (X) If Y = 2X + 5, find E[Y]A Consider that the variables X and Y have the following joint probability distribution. 1. 3. 0.05 0.05 0.00 0.05 0.10 0.20 0.10 0.35 0.10 (a) Find the marginal distribution of X (b) Find the marginal distribution of Y (c) Determine if X and Y are statistically independent. (d) Find P(Y = 1|X = 3).Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON