Explanation Given: The probability distribution of the random variable X is as follows, x − 3 − 1 0 1 3 5 P ( X = x ) 0.08 0.24 0.32 0.16 0.12 0.08 Table ( 1 ) Approach: The mean or the expected value of the random variable X is represented as μ , The μ can be obtained from probability distribution as, μ = x 1 p 1 + x 2 p 2 + ... + x n p n The variable is of a random variable X is represented as Var ( X ) , and it can be obtained as, Var ( X ) = p 1 ( x 1 − μ ) 2 + p 2 ( x 2 − μ ) 2 + ... + p n ( x n − μ ) 2 The standard deviation of a random variable X can be represented as σ , and it is defined by, σ = Var ( X ) Calculation: Consider table ( 1 ) , the mean of random variable X is,

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Author: Tan

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The mean, variance and standard deviation of the random variable X.

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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 deviation of the random variable X .

Solution Summary: The author calculates the mean, variance, and standard deviation of the random variable X.

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