The probability distribution of a random variable \( X \) is given below:\[\begin{array}{c|ccccc}x & 1 & 2 & 3 & 5 & 9 \\\hlineP(X = x) & \frac{3}{29} & \frac{5}{29} & \frac{10}{29} & \frac{9}{29} & \frac{2}{29} \\\end{array}\]The given mean \( \mu = 3.66 \).Find the variance (\(\text{Var}(X)\)) and the standard deviation, respectively. The options are:- [15.02, 3.88]- [500.00, 22.36]- [564.43, 23.76]- [3.88, 1.97]- [40.58, 6.37]

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A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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The probability distribution of a random variable X is given below. Given the mean Find the variance (Var(X)) and the standard deviation, respectively. O [15.02, 3.88] O [500.00, 22.36] O [564.43, 23.76] O [3.88, 1.97] O [40.58, 6.37] 1 2 3 5 10/29 5/29 X P(X=X) 3/29 H=3.66 9 9/29 2/29