1.

X is a random variable which can take the following values: (This is a table, c/2 means c over 2)

x.............0....1.....2...3....4

P(X=x)....c/2...c....2c..c...2/c

State the conditions for P(X = x) to be a probability distribution, then find the value of c for which this will be the case.

2.

The random variable X represents the number of visitors a hospital patient has in a visiting period. A maximum of four visitors is permitted. C is found to have probability distribution:

x...........0.......1......2......3.......4

P(X=x)..0.1....0.2....0.4....0.2....0.1

Show that E[X] = 2 and E [X²] = 5.2, then write down the probability distribution of the random variable Y = (X-2)² and hence, or otherwise, find E[(X-2)²].