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Probability Density Function
If you have ever taken a basic statistics class, you know this function better than you think. Remember standard deviations? How about when you calculated the odds between the standard and average deviation? Did you realize that you were using a calculus concept known as integrals? Now think about the space under the curve.
With this, we can assume that the space under the curve could be from negative infinity to positive infinity, or it could be a number set like the sides of a die.
But the value under the curve is one so you would be calculating the space under two points in the curve. If we go back to the sheet metal example, trying to find the odds that two errors occur is a bit of a trick question. These are discrete variables and not continuous.
A continuous value would be zero percent.
Since the value is discrete, the integer will be whole. There wouldn’t be any values between one and two, or between two and three. Instead, you would have 27% for two. If you wanted to know a value between two and three, what would the answer be?
PDF and the cumulative distribution function are able to take on continuous and discrete forms. Either way, you want to figure out how dense the odds are that fall under a range of points or a discrete point.
Cumulative Distribution Function
This function is the integral of the PDF. Both of these functions are used to provide random variables. To find the odds that a random variable is lower than a specific value you would us the cumulative distribution function.
The graph shows the cumulative probability. If you were looking at discrete variables, like the numbers on a die, you would receive a staircase looking graph. Every step up would have 1/6 of the value and the previous numbers.
Once you reach the sixth step, you would have 100%. This means that each one of the discrete variables has a 1/6 change of landing face up, and once it gets to the end the total is 100%.
