# Worksheet: Discrete Random Variables and Expected Value

Q1:

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

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

Find the mean number of cars per family.

• A
• B
• C
• D
• E

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 .

• A
• B
• C
• D
• E

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
• A
• B
• C15
• D

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
• A ,
• B ,
• C ,
• D ,

Q13:

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

 2 3 4 5
• A0
• B
• C
• D

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 .

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
• A ,
• B ,
• C ,
• D ,