Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
Start Practicing

Worksheet: Discrete Random Variables and Expected Value

Q1:

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

Number of Cars1234
Frequency1035155

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 .

1234
  • 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 .

123456

Q3:

The discrete random variable has the shown probability distribution.

123456
0.10.30.20.10.1

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?

2345
0.10.30.20.4

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 .

01234
0.30.3

Q10:

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

0123
0.30.2

Q11:

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

1346
  • A15
  • B
  • C
  • 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 .

1356
0.20.20.20.3
  • A,
  • B,
  • C,
  • D,

Q13:

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

2345
  • A
  • B
  • C0
  • D

Q14:

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

2345
0.10.30.20.4

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 .

1345
0.10.10.20.3
  • A,
  • B,
  • C,
  • D,