Find the following: a. Find the expectation of b. Find the variance of A discrete random variable X whose probability function is given by: f (x) = ( where x = 1, 2, 3, 4, 5
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- Find the marginal probabilities of each random variable X and Y in thefollowing table:- Compute the covariance and the correlation of these two random variables.Consider 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]O Prove that E(X) = E(X/Y), where X and Y are two random variables which are independent. %D
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- Consider a random sample from the distribution of Binomial, Poisson, Exponential, Gamma, and normal. Let T1 = X + 4 ; T2 = (X – 1); T3 = X1+4X2 – 3X3 & T4 = E7 X; /(n + 1). Find the MSE of each statistics and choose the best statistic.For a random variable X E(X) = 1.27, E(X²) = 3.79 The variance of X is equal to Select one: O 2.52 O 2.9843 O 2.1771 O 0.758 0.33513. Determine the value c so that each of the following functions can serve as probability distributions of the discrete random variable X: a. f(x) = c(x² +4) for x = 0,1, 2, 3; 3 b. f(x)%3Dс for x= 0,1, 2 3-x
- Compute the variance of the following probability distribution. If X is a random variable, then the variance is given by Var(X) = E (ײ) – [E(X)]². k Pr(X= k) 0 0.1 1 0.3 2 0.5 3 0.1 Var(X) = (Type an integer or a decimal.)Let a mixed random variable X have the following distribution. Find expectation of X. Find variance of X.Let X have beta distribution with a = 2 and B = 3. Then the mean and the variance of X, respectively, are Select one: O a. 0.04 and 0.4 O b. 0.02 and 0.04 O c. 0.4 and 0.04 O d. 0.4 and 0.20