Please answer these finite math questions. Topic is discrete random variables. Thanks!

If X is a random variable with probability distribution shown below, nd E(X). 3: a 0.4 :ij a. 0.8 O o. 1.0 if) D. 1.1 X is a discrete random variable with Pr[X = 2] = l and Pr[X = 1] = i. What is the variance of X'? 2 2 X is the number of heads obtained when a fair coin is tossed twice. Find E(X 3) O A. 2.75 I C) e. 1 C) e. 1.5 O n. -2.5 O E. 0.16 60% of the computer chips produced at a factory are good; the others are defective. A box contains 250 chips from the factor. Let X be the number of good chips in the box. What is cr(X) , the standard deviation of the number of good chips in the box? X is a discrete random variable whose mean is E(X) = 5 and whose variance is V(X) = 4. Y is another discrete random variable whose value is given by Y = -3X+ 20. What is the value of 00') '? O A -6 O B. 6 O c. 14 O D. 18 O E. 26 A certain experiment has 2 possible outcomes, 11 and {2. These outcomes are equally likely to occur when the experiment is performed. These are 2 discrete random variables dened for this experiment, X and Y. When outcome :1 occurs, X has the value 0 and Y has the value -2. When outcome t2 occurs, X has the value 1 and Y has the value 2. All of this information is summarized in the table shown below. Find o'(X+Y). outcome probability x y t. 1/2 0 -2 (2 1/2 1 2 O A. E 4 O B. j 2 9 Discrete random variable X has E(X) = 5 and V(X) = 3. Discrete random variable Y has EU) = 2 and V(Y) = 1. If X and Y are independent random variables, and W: 2X- 4)", nd V(W}. O a -4 O a. -2 O c. 2 O D. 10 O E. 28 Y is a continuous random variable with probability density function fYU) , where fy(y) =% if 0