EXERCISES. 1 Find the value of b and E(X) in these distributions

1 Find the value of b and E(X) in these distributions.

a)

	0.1	b	0.4	0.2

b)

	0.05	1.5	0.6	b	0.05

c)

	-3
	0.15	0.2	b	0.22	0.15

d)

	-4
	0.1	0.25	0.3	0.25	b

2 If three unbiased cubical dice are thrown, what is the expected number of threes that will occur?

3 A discrete random variable has a probability distribution function given by for

a) Find the value of c.

b) Find E(X).

4 Caroline and Lisa play a game that involves each of them tossing a fair coin.

The rules are as follows:

• If Caroline and Lisa both get heads, Lisa gains 6 points.

• If Caroline and Lisa both get tails, Caroline gains 6 points.

• If Caroline gets a tail and Lisa gets a head, Lisa gains 3 points.

• If Caroline gets a head and Lisa gets a tail, Caroline gains x points.

a) If X is the discrete random variable “Caroline’s gain”, find E(X) in terms of x.

b) What value of x makes the game fair?

5 A discrete random variable X can only take the values -1 and 1. If find the probability distribution for X.

6 A discrete random variable X can only take the values -1, 1 and 3. If and find the probability distribution for X.

7 A discrete random variable Y can only take the values 0, 2, 4 and 6. If and find the probability distribution for Y.

8 A five-a-side soccer team is to be chosen from four boys and five girls. If the team members are chosen at random, what is the expected number of girls on the team?

9 In a chemistry examination each question is a multiple choice with four possible answers. Given that Kevin randomly guesses the answers to the first four questions, how many of the first four questions can he expect to get right?

10 A discrete random variable X has probability distribution:

	0.1	0.2	0.35	0.25	0.1

Find:

a)

b)

c)

d)