4. A discrete random variable X has the probability distribution displayed in the table below, where 0 < <1

0	0.5	1	1.5	2
P (X=x)	p	p^2	2p^2	p

a. Find the value of .

b. Compute the expected value of .

5. Bonus question: A litter of eight mice consist of three females and five males. A random sample of four mice is taken from the litter for a particular experiment. Calculate the expected number of female mice in the sample. Calculate the variance of the number of female mice in the sample. Use some counting aid such as combinations/permutations to answer this question.

6. The random variable X can take only the values 0, 1, 2. Given that ( = 0) = ( = 1) = and that ( 2 ) = (), calculate the value of .

7. If has range space = {0, 1}, show that ( 2 ) = 0.