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Worksheet: Discrete Random Variables and Expected Value
Q11:
The function in the given table is a probability function of a discrete random variable . Find the expected value of .
| 0 | 1 | 2 | 3 | 4 | |
| 0.1 | 0.1 | 0.4 | 0.2 |
Q12:
Let denote a discrete random variable which can take the values . Given that has probability distribution function , find the expected value of .
- A
- B
- C1
- D
Q13:
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 |
Q14:
Work out the expected value of the random variable whose probability distribution is shown.
Q15:
Let denote a discrete random variable which can take the values 1, 2, 3, 4, and 5. Given that , , , and , find the expected value of .
- A
- B
- C16
- D
Q16:
Work out the expected value of the random variable whose probability distribution is shown.
Q17:
Let denote a discrete random variable which can take the values 4, 5, 8, and 10. Given that , , and , find the expected value of . Give your answer to two decimal places.
Q18:
Let denote a discrete random variable which can take the values , 0, and 5. Given that the expectation of is 0.03 and , find .
- A
- B
- C
- D
Q19:
The discrete random variable has the shown probability distribution.
| 1 | 2 | 3 | 4 | |
Find the value of .
- A
- B
- C
- D
- E
Hence, determine the expected value of .
- A
- B
- C
- D
- E
Q20:
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
Q21:
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 .
Q22:
A discrete random variable has a uniform probability distribution such that , where . Determine .
Q23:
23 students took an exam; 7 students got 3 marks, 8 students got 8 marks, and 8 students got 2 marks. Given that denotes the number of marks received, find the expected value of . If necessary, round your answer to the nearest hundredth.
Q24:
Work out the expected value of the random variable whose probability distribution is shown.
Q25:
Scarlett had a spinner with ten equal sections labeled with the numbers 1 to 10. She spun it 300 times and recorded the outcomes in a frequency table.
| Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Frequency | 35 | 27 | 22 | 11 | 24 | 28 | 33 | 35 | 49 | 36 |
If the spinner was fair, how many times would you expect to see each number if you spun it 300 times?
State whether the spinner is biased and why.
- AThe spinner is biased because the number 4 only appeared half as often as expected and the number 9 appeared much more often than expected.
- BThe spinner is biased because the numbers did not appear exactly 30 times each.
- CThe spinner is not biased because most of the numbers appeared around 30 times.