1. Two coins are tossed and the number of heads is recorded.
Let X be a discrete random variable, where X is the number of heads.
a. Use the formula for x = 1, 2, 3 to complete the table below.
(Remember that 0! = 1 and 1! = 1 and 2! = 2)
x

0

1

2

P(X = x)

b. Draw a vertical line graph to show this probability function.
2. The discrete random variable X has a probability distribution as follows:
x

3

4

5

6

7

P(X = x)

0.2

0.3

z

0.15

0.25

a. Find the value of z
b. Find P(4 ≤ X ≤ 6)
c. Find P(X < 5)
d. Draw a vertical line graph to show this distribution.
3. 
Draw probability distribution tables for the following experiments:

4. The random variable Y has the following probability distribution:
y

2

4

6

8

P(Y = y)

3k

2k

k

4k

Find the value of k.
5. One of the values in this probability distribution table for the random variable Z is wrong.
z

10

11

12

13

P(Z = z)

0.2

0.3

1.1

0.4

a. Which value is wrong?
b. What should the correct value be?
6. The probability function for a discrete random variable W is shown below.
w

2

1

0

1

2

P(W = w)

0.25

0.1

0.2

0.3

0.15

If X = W^{2} show the probability distribution for the random variable X.
7. A wardrobe contains a drawer with 4 pairs of red socks and 6 pairs of green socks.
A pair of socks is taken out at random, and the colour noted and the socks are put back in the drawer. This is repeated 3 more times for a total of 4 pairs of socks.
Let Y be the random variable where Y = the number of red socks taken out of the drawer.
Draw a probability distribution table to show this.
8. The formula for a probability function is P(X = x) = kx for x = 4, 5 and 6
What is the value of k?