Exercise 1. Three balls are randomly chosen with replacement from an urn containing 5 blue, 4 red, and 2 yellow balls. Let X denote the number of red balls chosen.
(a) What are the possible values of X?
(b) What are the probabilities associated to each value?
Exercise 2. Suppose X is a random variable such that E[X] = 50 and Var(X) = 12. Calculate the following quantities.
(a)
(b)
![E[X^2]](https://s0.wp.com/latex.php?latex=E%5BX%5E2%5D&bg=ffffff&fg=333333&s=0&c=20201002)
![E [2X + 2]](https://s0.wp.com/latex.php?latex=E+%5B2X+%2B+2%5D&bg=ffffff&fg=333333&s=0&c=20201002)
(c)
![E [(X+2)^2]](https://s0.wp.com/latex.php?latex=E+%5B%28X%2B2%29%5E2%5D&bg=ffffff&fg=333333&s=0&c=20201002)
(d) Var[−X]
Research and Lecture notes 