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In this lesson, we will learn how to calculate the variance and standard deviation of a probability distribution.

Q1:

The function in the given table is a probability function of a discrete random variable π . Find the standard deviation of π . Give your answer to two decimal places.

Q2:

Q3:

The function in the given table is a probability function of a discrete random variable π . Given that the expected value of π is 6.5, find the standard deviation of π . Give your answer to two decimal places.

Q4:

The function in the given table is a probability function of a discrete random variable π . Find the variance of π . If necessary, give your answer to two decimal places.

Q5:

The function in the given table is a probability function of a discrete random variable π . Given that the expected value of π is 9 2 , find the variance of π . Give your answer to two decimal places.

Q6:

Can the function in the given table be a probability distribution function?

Q7:

A die is rolled two successive times. If the random variable π denotes the sum of numbers appearing on the upper face after each roll, find the range of π .

Q8:

Let π denote a discrete random variable which can take the values 0 , 2 , 5 a n d . Given that π has probability distribution function π ( π₯ ) = π 6 π₯ + 6 , find the standard deviation of π . Give your answer to 2 decimal places.

Q9:

Let π denote a discrete random variable which can take the values β 2 , β 1 , π , 2 a n d . Given that π has probability distribution function π ( π₯ ) = π₯ + 4 1 6 , find the variance of π .

Q10:

Let denote a discrete random variable which can take the values 2, 4, and 5. Given that has probability distribution function , find the variance of . If necessary, give your answer to two decimal places.

Q11:

Given that V a r ( π ) = 2 8 , find V a r ( 4 π + 9 ) .

Q12:

Let π denote a discrete random variable which can take the values β 2 , 2 , 4 5 a n d . Given that π ( π = β 2 ) = 0 . 1 5 , π ( π = 2 ) = 0 . 4 3 , and π ( π = 4 ) = 0 . 2 5 , find the value of π ( π > 2 ) .

Q13:

Let π denote a discrete random variable which can take the values 3, 5, and 6. Which of the following functions could represent the probability function of π ?

Q14:

Which of the following is not a discrete random variable?

Q15:

Let π denote a discrete random variable which can take the values 2, 6, 7, and 8. Given that π ( π = 2 ) = π ( π = 6 ) = 3 2 2 and π ( π = 7 ) = 4 1 1 , find π ( π = 8 ) . Give your answer as a fraction.

Q16:

Let π denote a discrete random variable which can take the values 1 , 2 , 3 , 4 , 5 a n d . Given that π has probability distribution function π ( π₯ ) = π + π₯ 1 6 , find the value of π .

Q17:

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

Q18:

Let π denote a discrete random variable which can take the values 1 , 2 , 3 4 a n d . Given that π ( π = 1 ) = 0 . 4 6 , π ( π = 2 ) = 0 . 1 8 , and π ( π = 3 ) = 0 . 1 4 , find the value of π ( π = 4 ) .

Q19:

Let π denote a discrete random variable which can take the values 0, 1, 3, and 4. Given that π ( π₯ = 0 ) = π 1 0 , π ( π₯ = 1 ) = π β 4 1 0 , π ( π₯ = 3 ) = 9 π + 2 1 0 , and π ( π₯ = 4 ) = 1 0 π + 3 1 0 , find the value of π .

Q20:

Let π denote a discrete random variable which can take the values 1, 2, 3, 4, 5, and 6. Given that π has probability distribution function π ( π₯ ) = π π₯ 5 , find the value of π .

Q21:

Let π denote a discrete random variable which can take the values 1 , π , 7 a n d . Given that π has probability distribution function π ( π₯ ) = π₯ + 2 1 8 , find the variance of π . Give your answer to two decimal places.

Q22:

Let denote a discrete random variable which can take the values 3, 4, and 5. Given that , find the variance of . If necessary, give your answer to two decimal places.

Q23:

Let π denote a discrete random variable which can take the values 2, 3, 5, and 8. Given that π ( π = 2 ) = 1 2 4 , π ( π = 3 ) = 5 1 2 , π ( π = 5 ) = 3 8 , and π ( π = 8 ) = 1 6 , find the variance of π . Give your answer to two decimal places.

Q24:

Let π denote a discrete random variable which can take the values 0 , 2 , 5 a n d . Given that π has probability distribution function π ( π₯ ) = π 6 π₯ + 6 , find the variance of π .

Q25:

Let π denote a discrete random variable which can take the values 1, 2, 7, and 8. Given that π ( π = 1 ) = 8 3 , π ( π = 2 ) = 4 9 , and π ( π = 7 ) = 1 1 8 , find the variance of π . Give your answer to two decimal places.

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