The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season. X 0 1 2 3 4 5 D P(x) 0.1674 0.3428 0.2908 0.1497 0.0379 0.0114 The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random var X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean a standard deviation. What property is being illustrated? Click the icon to view the data tables. Data Tables Compute the theoretical mean of the random variable X for the given probability distribution. Hx 1.582 hits = = (Round to three decimal places as needed.) Compute the theoretical standard deviation of the random variable X for the given probability distribution. 0x = 1.114 hits (Round to three decimal places as needed.) Approximate the mean of the random variable X based on the simulation for 25 games. xx hits (Round to three decimal places as needed.) Table of the numbers of hits for 25 games 3 14 1 0 1 135 0 11423 212 3 1 01 1 2 1 Table of the numbers of hits for 50 games 3141011350 11 4 2 3 2 123 1 011 2 1 0 2 3 0 1 1 22111 2010 2 1 3 2 2 2 2003 - X