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Worksheet: Discrete Random Variables and Expected Value

Practice calculating the expected value for a probability distribution in this worksheet. Calculate the expected value from both a table and a graph and challenge yourself to calculate the variance for a probability distribution.

Q1:

The frequency table shows the number of cars that 65 families have.

Number of Cars	1	2	3	4
Frequency	10	35	15	5

Find the mean number of cars per family.

This data can be expressed as a probability distribution for the discrete random variable as shown. Find the value of , , , and .

	1	2	3	4

A , , ,
B , , ,
C , , ,
D , , ,
E , , ,

Calculate the expected value of .

Q2:

The table shows the probability distribution of a fair six-sided die. Determine .

	1	2	3	4	5	6

Q3:

The discrete random variable has the shown probability distribution.

	1	2	3	4	5	6
	0.1	0.3	0.2	0.1	0.1

Find the value of .

Hence, determine the expected value of .

Q4:

An experiment produces the discrete random variable that has the probability distribution shown. If a very high number of trials were carried out, what would be the likely mean of all the outcomes?

	2	3	4	5
	0.1	0.3	0.2	0.4

Q5:

Work out the expected value of the random variable whose probability distribution is shown.

Q6:

Work out the expected value of the random variable whose probability distribution is shown.

Q7:

Work out the expected value of the random variable whose probability distribution is shown.

Q8:

Work out the expected value of the random variable whose probability distribution is shown.

Q9:

The function in the given table is a probability function of a discrete random variable . Find the value of .

	0	1	2	3	4
		0.3	0.3

Q10:

The function in the given table is a probability function of a discrete random variable . Find the value of .

		0	1	2	3
		0.3	0.2

Q11:

The function in the given table is a probability function of a discrete random variable . Find the expected value of .

	1	3	4	6

Q12:

The function in the given table is a probability function of a discrete random variable . Given that the expected value of is 4, find the values of and .

	1	3		5	6
	0.2	0.2		0.2	0.3

Q13:

The function in the given table is a probability function of a discrete random variable . Find the value of .

	2	3	4	5

Q14:

An experiment that produces the discrete random variable has the probability distribution shown.

	2	3	4	5
	0.1	0.3	0.2	0.4

Calculate .

The variance of can be calculated using the formula . Calculate to 2 decimal places.

Q15:

The function in the given table is a probability function of a discrete random variable . Given that the expected value of is 4.8, find the values of and .

	1	3	4	5
	0.1	0.1	0.2	0.3