Let X and Y have the joint probability distribution as following Y 0 1 3 a 0.2 0.1 0.3 0.2 0.1 (1) Find a; (2) Get the marginal probability distributions of (X,Y) (3) Determine if X and Y are independent or not 1.
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- 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(-1A 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).Choose ALL THE CORRECT STATEMENTS in the following ones about probability distribution. i. Probability mass function indicates the probability distribution of a continuous random variable. ii. Probability mass function indicates the probability distribution of a discrete random variable. iii. The probability mass function of a discrete random variable X at a is denoted by P(X < a). iv. The probability function of a continuous random variable Y can be described by using P(Y= a).Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 0Let X and Y have the following joint distribution:X \Y 0 1 2 0 2/12 1/12 5/12 1 1/12 1/12 2/12(a) Find the probability distribution of X|Y = 0, and E[X|Y = 0].(b) Find E[Y ] and E[X].(c) Find the probability that Y is larger than zero.(d) Are X and Y dependent? Justify your answerSuppose X and Y have the following joint distribution: (please refer to image attached) Find the distributions of X and Y. Find Cov (X, Y), i.e. the covariance of X and Y. Find p(X, Y), i.e. the correlation of X and Y.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