Question 1. A random variable X has the following probability mass function:

x ->. 8 6 0 4 6 9

P (X = x) - >. 0.259 0.055 0.225 0.082 0.197 0.182

(a) Write down the set X. (b) Determine E(X), Var(X) and SD(X).

Let A denote the event "X = 0", let B denote the event "6 X < 9", and let C denote the event "X is positive". Note: zero is neither positive nor negative.

(c) Use set operations (union, intersection, complements) to express the following events in terms of A, B and C: (i) X is not equal to zero.

(ii) X is a negative number. (iii) X = 9

You do not need to do any calculations for part (c).

(d) Determine each of the following: (i) P(A), P(B) and P(C)

(ii) P(Ac Cc), P(BC) and P(BCc) (iii) P(AcCc),P(BC)andP(BCc) (iv) P(Ac |Cc),P(C|B)andP(A|Cc)

Complete Question 1 by hand, showing all working. Give numeric answers to at least 3 decimal places