Explanation Given: The table for probability distribution of a random variable X is shown below. x − 198 − 195 − 193 − 188 − 185 P ( X = x ) 0.15 0.30 0.10 0.25 0.20 Approach: The mean of a random variable X is given by, μ = x 1 p 1 + x 2 p 2 + x 3 p 3 + … + x n p n Here, x 1 , x 2 , x 3 , … , x n are values of random variable X with probabilities p 1 , p 2 , p 3 , … , p n respectively. The variance of a random variable X is given by, Var ( X ) = p 1 ( x 1 − μ ) 2 + p 2 ( x 2 − μ ) 2 + p 3 ( x 3 − μ ) 2 + … + p n ( x n − μ ) 2 The standard deviation of a random variable X is given by, σ = Var ( X ) Calculation: Substitute − 198 for x 1 , − 195 for x 2 , − 193 for x 3 , − 188 for x 4 , − 185 for x 5 , 0.15 for p 1 , 0.30 for p 2 , 0.10 for p 3 , 0.25 for p 4 and 0.20 for p 5 in above mentioned formula of mean. μ = ( − 198 ) ( 0.15 ) + ( − 195 ) ( 0.30 ) + ( − 193 ) ( 0.10 ) + ( − 188 ) ( 0.25 ) + ( − 185 ) ( 0

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Chapter 8.3, Problem 6E

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Ch. 8.1 - What is a random variable? Give an example.Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Three balls are selected at random without...Ch. 8.1 - 2.A coin is tossed four times. Let the random...Ch. 8.1 - A die is rolled repeatedly until a 6 falls...Ch. 8.1 - Cards are selected one at a time without...Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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The mean, variance and standard deviations of X .

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The mean, variance and standard deviations of X .

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To find: The mean, variance and standard deviations of X.

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Chapter 8 Solutions

To find:

The mean, variance and standard deviations of X.