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Consider the discrete random variable XX given in the table below. Calculate the mean, variance, and standard deviation of XX. Round answers to two decimal places.\newline \begin{array}{c|c} X & P(X) \ \hline 1 & 0.68 \ 11 & 0.11 \ 15 & 0.12 \ 17 & 0.09 \ \end{array} \newline\begin{array}{c} \mu= \ \sigma^{2}= \ \sigma= \ \end{array}\newlineWhat is the expected value of XX ?

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Q. Consider the discrete random variable XX given in the table below. Calculate the mean, variance, and standard deviation of XX. Round answers to two decimal places.\newline \begin{array}{c|c} X & P(X) \ \hline 1 & 0.68 \ 11 & 0.11 \ 15 & 0.12 \ 17 & 0.09 \ \end{array} \newline\begin{array}{c} \mu= \ \sigma^{2}= \ \sigma= \ \end{array}\newlineWhat is the expected value of XX ?
  1. Calculate expected value: Calculate the expected value (mean) of XX. The expected value of a discrete random variable XX is calculated by summing the products of each possible value of XX and its corresponding probability. So, we calculate the mean (μ\mu) as follows: μ=Σ[X∗P(X)]=(1∗0.68)+(11∗0.11)+(15∗0.12)+(17∗0.09)=0.68+1.21+1.8+1.53=5.22\mu = \Sigma[X * P(X)] = (1 * 0.68) + (11 * 0.11) + (15 * 0.12) + (17 * 0.09) = 0.68 + 1.21 + 1.8 + 1.53 = 5.22
  2. Calculate variance: Calculate the variance (σ2\sigma^2) of XX. The variance is calculated by summing the products of the square of the difference between each value of XX and the mean, and its corresponding probability. $\sigma^\(2\) = \Sigma[(X - \mu)^\(2\) * P(X)] = (\(1\) - \(5\).\(22\))^\(2\) * \(0\).\(68\) + (\(11\) - \(5\).\(22\))^\(2\) * \(0\).\(11\) + (\(15\) - \(5\).\(22\))^\(2\) * \(0\).\(12\) + (\(17\) - \(5\).\(22\))^\(2\) * \(0\).\(09\) = (\(4\).\(22\))^\(2\) * \(0\).\(68\) + (\(5\).\(78\))^\(2\) * \(0\).\(11\) + (\(9\).\(78\))^\(2\) * \(0\).\(12\) + (\(11\).\(78\))^\(2\) * \(0\).\(09\) = \(17\).\(8084\) * \(0\).\(68\) + \(33\).\(4084\) * \(0\).\(11\) + \(95\).\(5684\) * \(0\).\(12\) + \(138\).\(7684\) * \(0\).\(09\) = \(12\).\(109712\) + \(3\).\(674924\) + \(11\).\(468208\) + \(12\).\(489056\) = \(39\).\(7419\)
  3. Calculate standard deviation: Calculate the standard deviation (\(\sigma\)) of \(X\). The standard deviation is the square root of the variance. \(\sigma = \sqrt{\sigma^2} = \sqrt{39.7419} = 6.30\) (rounded to two decimal places)

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