Question

The upper red signs are the questions I'm confused about. Thanks.

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 0 1 2 3 4 х P(x) 0.2009 0.3224 0.3024 0.1378 0.0351 0.0014 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 variable 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 and standard deviation. What property is being illustrated? Click the icon to view the data tables. Approximate the mean of the random variable X based on the simulation for 50 games. Hx1.500 hits (Round to three decimal places as needed.) Approximate the standard deviation of the random variable X based on the simulation for 50 games. Ox1.082 hits (Round to three decimal places as needed.)

Answer 1

x	P(x)	x*P(x)	x^2*P(x)
0	0.2009	0	0
1	0.3224	0.3224	0.3224
2	0.3024	0.6048	1.2096
3	0.1378	0.4134	1.2402
4	0.0351	0.1404	0.5616
5	0.0014	0.007	0.035
sum	1	1.488	3.3688

#mean

$\mu$x=$\sum x*p(x)$

$\mu$x=1.488

# standard deviation

$\sigma x=\sqrt{\sum x^2p(x)-\mu x^2}$

$\sigma x=\sqrt{3.3688-1.488^2}$

$\sigma x=1.155$