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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:
Q4:
Q5:
Q6:
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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