## Probability Distribution Exercise

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: a. The number of heads when three coins are tossed. b. The sum of the scores when two six-sided dice are thrown c. The difference between the highest number and lowest number when two dice are thrown (use 0 if each die is same) 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 = W2 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?