The main takeaway from this section should be knowing how to calculate and interpret the standard deviation and mean.
Center of a Discrete Random Variable
Mean or Expected value of a discrete variable is its average value over many, many repetitions of the same chance process. To find the mean or expected value of X, multiply each possible value of X by its probability and then add all of the products.
The mean is the balance point of a distribution. Formula: Summation(xi*pi)= mean of X
Critical Tip: DO NOT write the mean of a random variable as a non integer value if it is a decimal because almost all expected values are decimals.
Variability of a Discrete Random Variable
The standard deviation of a discrete random variable measures how much the values of the variable typically vary from the mean.
The variance of X is SD^2= summation(xi-mean of x)^2 * pi .
The standard deviation of X is the square root of the variance so SD = sqrt(summation(xi-mean of x)^2 * pi).
If you decide to use your calculator, make sure you list how you got to your answer. Use context and don’t just put a number down as the answer. Show work to maximize the amount of points you get.