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In this lesson, we will learn how to calculate the expected value from both a table and a graph and learn how to calculate the variance for a probability distribution.

Q1:

The table shows the probability distribution of a fair six-sided die. Determine πΈ ( π ) .

Q2:

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

Q3:

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

Q4:

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Calculate πΈ ( π ) .

Calculate πΈ οΉ π ο 2 .

The variance of π can be calculated using the formula V a r ( π ) = πΈ οΉ π ο β πΈ ( π ) 2 2 . Calculate V a r ( π ) to 2 decimal places.

Q9:

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

Q10:

The function in the given table is a probability function of a discrete random variable π . Given that the expected value of π is 2 5 4 5 7 , find the value of π΅ .

Q11:

Q12:

Let π denote a discrete random variable which can take the values β 1 , π , 1 a n d . Given that π has probability distribution function π ( π₯ ) = π₯ + 2 6 , find the expected value of π .

Q13:

An experiment produces the discrete random variable π 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?

Q14:

Q15:

Let π denote a discrete random variable which can take the values 1, 2, 3, 4, and 5. Given that π ( π = 1 ) = 7 3 3 , π ( π = 2 ) = 8 3 3 , π ( π = 3 ) = 1 1 1 , and π ( π = 4 ) = 1 3 3 , find the expected value of π .

Q16:

Q17:

Let π denote a discrete random variable which can take the values 4, 5, 8, and 10. Given that π ( π = 4 ) = 4 2 7 , π ( π = 5 ) = 5 2 7 , and π ( π = 8 ) = 8 2 7 , find the expected value of π . Give your answer to two decimal places.

Q18:

Let π denote a discrete random variable which can take the values β 2 , 0, and 5. Given that the expectation of π is 0.03 and π ( π = β 2 ) = 9 2 5 , find π ( π = 5 ) .

Q19:

The discrete random variable π has the shown probability distribution.

Find the value of π .

Hence, determine the expected value of π .

Q20:

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

Find the mean number of cars per family.

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

Calculate the expected value of π .

Q21:

Q22:

A discrete random variable π has a uniform probability distribution such that π ( π = π₯ ) = 1 1 1 , where π₯ β { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 1 0 , 1 1 } . Determine πΈ ( π ) .

Q23:

23 students took an exam; 7 students got 3 marks, 8 students got 8 marks, and 8 students got 2 marks. Given that π denotes the number of marks received, find the expected value of π . If necessary, round your answer to the nearest hundredth.

Q24:

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.

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.

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