What is function learning?

What is the use of Probability distribution Function and cumulative distribution function in machine learning concepts?

• Answer:

  So let me first say that the question is wrong somewhat. There is no such thing as a Probability Distribution function. But that is OK. Many people are confused between PMF(Probability Mass Function), PDF(Probability Density Function) and CDF(Cumulative Distribution Function). Probability Mass Function (PMF) is defined for a discrete random Variable and provides what is the probability of X being a certain value. It is just a regular function in the sense that it takes as parameter a value and provides the probability that random variable attains that Value. So lets say we have a probability Mass function of a discrete random variable X called P(X=k), then P(X=27) will tell me the probability that the random Variable will take the value 27 Cumulative Density Function does actually what it says. It is cumulative. So if we define a CDF as F(x) = P(X<=x). Therefore F(27) = P(X<=27) = P(X=0) + P(X=1) + P(X=2) + P(X=3) +.+.+ P(X=27) i.e. F(27) will tell me the probability that a random variable is less than or equal to 27. Probability Density Function (PDF) is defined for a Continuous random Variable and it is different from the other two in a sense that it is not Probability. It is instead a density function. We cannot define a PMF for a continuous RV as P(X=x) will equal 0 in case of continuous RV. But we can find the probability that X falls between (x-e/2,x+e/2) by saying that P(x-e/2<=X<=x+e/2) = f(x)*e i.e we multiply the probability density function, f by a range to get Probability.