4.8 Mean and Standard Deviation of Random Variables

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.

🎥Watch: AP Stats - Probability: Random Variables, Binomial/Geometric Distributions

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