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?