ProbabilityDensityFunctions.md (1312B)
1 # Probability Density Functions (PDFs) 2 3 Stats ch1 4 5 **Definition:** A probability density function shows the probability of outcomes for [ContinuousProbability](ContinuousProbability.md) problems. 6 7 **Important:** PDFs are for continuous random variables whereas PMFs are for discrete. 8 9 Think of KDEs and kind of histograms. The difference with histograms is they use bins instead of a continuous probability graph. 10 11 Something to note, the area under the curve is the probability. As such, the likelihood of all values that come before some value is the integral over said range (Antiderivative. See fundamental theroem of calculus). 12 13 Another property of a PDF is that the integral of -infinity to infinity is always equal to 1 and p(y) >= 0 for all y. This means there is never a negative probability and there is a 100% probability across the domain of the function. 14 15 ## Percent Calculation 16 17 The integral along a specified range is the probability of something happening in that range. This is thought of as the area below the curve for the specified range. 18 19 An interesting thing about this is that any given point, given that it is uncountable, will have a p(x) = 0, but when calculating the area we find a value. 20 21 Additionally, we find that the integral of the function from -inf to inf is always equal to 1.