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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:

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Q7:

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.

Q8:

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

Q9:

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 ) .

Q10:

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 distribution function of π ?

Q11:

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

Q12:

Which of the following is not a discrete random variable?

Q13:

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.

Q14:

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.

Q15:

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 .

Q16:

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 .

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 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.

Q19:

Let π denote a discrete random variable which can take the values 1 , 2 , 3 , 5 a n d . Given that π has probability distribution function π ( π₯ ) = π 1 0 π₯ + 1 0 , find the standard deviation of π . Give your answer to 2 decimal places.

Q20:

Let π denote a discrete random variable which can take the values β 1 , 1 , 4 a n d . Given that π has probability distribution function π ( π₯ ) = π 9 π₯ + 1 8 , find the standard deviation of π . Give your answer to 2 decimal places.

Q21:

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 .

Q22:

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

Q23:

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.

Q24:

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.

Q25:

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