1. If X is the r.v. the number on a biased die, and the p.d.f. of X is as shown, x 1 2 3 4 5 6 P(X = x) 1/6 1/6 1/5 y 1/5 1/6

Find

(a) the value of y,

2. A variable X has a probability distribution shown in the table below:

Value of X	1	2	5	10
Probability	0.5	0.3	p	q

Given that X can only takes the values 1, 2, 5 or 10, and E(X) = 2.5, calculate

1. the value of p and of q,
2. the variance of X,
3. the standard deviation of X.