Probability: Average Value (or Mean Value)

In this video I go over deriving the average value when given the probability density function of a random continuous variable. In this case, I use the random variable being the call waiting time whenever you goal a company, i.e. calling their customer support phone-line. Using the long-run proportion as the basis of the probability we can thus approximate the total wait time by looking at the area under the graph multiplied by the number of experimental data we have, in this case the number of callers. The average wait time would thus just be the total time waited by all callers divided by the number of callers. This result, which is written as an integral, is also the x-coordinate of the centroid, or center of mass, of the region underneath the probability density function.

The average value, is also called the mean value and is traditionally written by the greek letter mu, μ.

This is a very in-depth video on determining the average value of any given probability density function so make sure to watch it!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhr8xfltWIER_ncymZA

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