Master Statistics and Probability Problems with Expert Help

Let X be a random variable with probability density function.
$f(x)=\{\begin{array}{l}c(1-x^2)-1<x<1\\ 0\text{ otherwise}\end{array}$
(a) What is the value of c? (b) What is the cumulative distribution function of X?

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.

$\begin{array}{|cc|}\hline x& P(x)\\ 0& 0.167\\ 1& 0.3289\\ 2& 0.2801\\ 3& 0.149\\ 4& 0.0382\\ 5& 0.0368\\ \hline\end{array}$
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?
a) Compute the theoretical mean of the random variable X for the given probability distribution.
${\displaystyle \mu =?}$
b) Compute the theoretical standard deviation of the random variable X for the given probability distribution.
${\displaystyle \sigma =?}$
c) Approximate the mean of the random variable X based on the simulation for 25 games.
${\displaystyle \bar{X}=?}$
d) Approximate the standard deviation of the random variable X based on the simulation for 25 games.
${\displaystyle S=?}$

The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high school preparation class, and no preparation class. Use the information from the table to answer the remaining questions. 
$\begin{array}{|cccc|}\hline \text{Treatment}& \text{Number of Observations}& \text{Sample Mean}& \text{Sum of Squares (SS)}\\ \text{Private prep class}& 60& 680& 265,500.00\\ \text{High school prep class}& 60& 650& 276,120.00\\ \text{No prep class}& 60& 635& 302,670.00\\ \hline\end{array}$ 
Using the data provided, complete the partial ANOVA summary table that follows (Hint: T, the treatment total, can be calculated as the sample mean times the number of observations G, the grand total, can be calculated from the values of T once you have calculated them.) 
$\begin{array}{|cccc|}\hline \text{Source}& \text{Sum of Squares (SS)}& df& \text{Mean Square (MS)}\\ \text{Between treatments}& & & \\ \text{Within treatments}& & & \\ \hline\end{array}$ 
ANOVA summary tables typically have a "Total" row not induded in the partial table you just completed. Which of the following is a possible reason for induding this row? 
a) The ${\displaystyle M{S}_{\to tal}}$ is used in the calculation of the F test statistic. 
b) The ${\displaystyle S{S}_{\to tal}}$ is used in the calculation of the F test statistic. 
c) The total sums of squares is the sometimes called the "error term" 
d) The $S{S}_{total}$ is sometimes easier to calculate than. $S{S}_{between}$ Since $S{S}_{within}+S{S}_{between}=S{S}_{total}$, you can use $S{S}_{total}$ to calculate $S{S}_{between}$.
In ANOVA, the F test statistic is the ? of the between-treatments variance and the within-treatments variance. the value of the F test statistic is ? 
When the null hypothesis is true, the F test statistic is ? When the null hypotesis is false, the F test statistic is most likely ? In general, you should reject the null hypotesis for.