The random variables A and B have variances 0.2 and 0.5 respectively. Let T= 5A+2B. The variance of T is 6 O a. False O b. True
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- If X and Y are independent, normally distributed random variables each with mean 0 and variance 1, then 2X + 2Y: Select one: a. has a normal distribution with mean 2 and variance 10 b. has a normal distribution with mean 2 and variance 8 c. has a normal distribution with mean 0 and variance 10 d. has a normal distribution with mean 0 and variance 8 e. has a normal distribution with mean 0 and variance 5Let the random variables X and Y have the joint p.m.f. x+ y f (x, y) = 32 x = 1, 2, y = 1,2,3,4. Find the means lx and uy, the variances oy and oý, and the correlation coefficient p. Are X and Y independent or dependent? 6.Let X, and X, be independent random variables with mean u and variance o?. Suppose that we have two estimators of u: 3X, -X, and 9,* ,then the variance of each estimator is 3 2
- Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance a. Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance b. multiplied by the product of the standard deviations for x and y. c. multiplied by the standard deviation of y and divided by the standard deviation of x. d. multiplied by the standard deviation of x and divided by the standard deviation of y.The random variables A and B have variances 0.2 and 0.5 respectively. Let T= 5A+2B. The variance of T is 6 a. True b. False <ANSWERS ALL PARTS A,B,C A) Roll a dice, X=the number obtained. Calculate E(X), Var(X). Use two expressions to calculate variance. B) Two fair dice are tossed, and the face on each die is observed. Y=sum of the numbers obtained in 2 rolls of a dice. Calculate E(Y), Var(Y). C) Roll the dice 3 times, Z=sum of the numbers obtained in 3 rolls of a dice. Calculate E(Z), Var(Z) from the result of part a and b.
- 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 0.20Kk.340.Let X be a random variable and Y = aX + b with a ̸= 0. Show that the correlation between X and Y is either +1 or −1. State the conditions which make the correlation equal to +1.