Hello, my name is Walter Unglaub and this is standard deviants in calculus. So a standard deviation in probability and statistics is a associated with the variation or spread or dispersion in other words of a particular probability distribution of a random variable x. So here half the height, half the maximum of the probability distribution, I have a certain spread and the spread, the standard deviation is typically denoted using the Greek letter sigma. Lowercase sigma. Now calculus, which concerns itself with the study of continuous variables we can use we can derive and right down an equation for the standard deviation in terms of an integral. If you had a discreet set of data points you would be writing the definition in terms of a sum but we're going to assume we have a continuous probability density function or PDF for short and it's a probability density function in terms of x or random variable. So the definition for the standard deviation will be equal to the square root of the integral over x of x minus mu where mu is the average or mean. So here mu is equal to this point in x for this normal distribution times the probability distribution in x, dx. So this is our definition for the standard deviation for a continuous random variable and we can define and calculate the average value for this distribution in x in terms of another integral. So mu, the mean or average is defined as the integral over x of x times p of x dx. Where x is a random variable and this is the probability distribution. My name is Walter Unglaub and this is standard deviants in calculus.
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A standard deviation in probability and statistics is a associated with the variation or spread or dispersion in other words of a particular probability distribution of a random variable x. Find out about standard deviants in calculus with help from an educator with years of experience in this free video clip.
Expert: Walter Unglaub
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Series Description: Understanding physics will require you to understand a number of very important concepts at the subject's core. Find out about physics and calculus with help from an educator with years of experience in this free video series.
A standard deviation in probability and statistics is a associated with the variation or spread or dispersion in other words of a particular probability distribution of a random variable x. Find out about standard deviants in calculus with help from an educator with years of experience in this free video clip.