Question

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?

Answer 1

Answer:

Hello here is the missing data to your question

x  P(x)

0  0.167

1  0.3289

2  0.2801

3  0.149

4  0.0382

5  0.0368

The theoretical values are lower than the approximate values and the property illustrated is the mean and standard deviation

A) 1.6729

B)  1.234061

C) 1.84

D)  1.462874

Step-by-step explanation:

A) calculate the theoretical mean

theoretical mean (u) = summation of ; $x_{i}p(x_{i})$

                 = 0(0.167)+1(0.3289)+2(0.2801)+3(0.149)+4(0.0382)+5(0.0369)

                 = 1.6729

B) calculate the theoretical standard deviation

     theoretical standard deviation = $\sqrt{variance}$ = $\sqrt{[summation of x_{i}^2 p(x_{i} ) ]-u^2}$

= $\sqrt{[0+0.3289+1.1204+1.341+0.6112+0.92]-(2.798594)}$

= 1.234061

C) calculate the approximate mean

the generated data used for calculation is added below

mean (x) = $\frac{summation of (x_{i}) }{n}$ = $\frac{1+2...+2+1}{25}$ = 46/25 = 1.84

D) calculate the approximate standard deviation

std = $\sqrt{variance}$

     = $\sqrt{\frac{summation of( x_{i}-x )^2}{n-1} }$

    = $\sqrt{2.14}$ = 1.462874