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Worksheet: Discrete Random Variables and Expected Value

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.

  • 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 ,