Question

Summarize key data distribution concepts including probability mass functions (PMF), probability density functions (PDF), and cumulative distribution functions (CDF). Based on an organization or any organization you are most familiar with, provide an example of a PMF, an example of a PDF, and an example of a CDF, based on the type of data used in the organization. How would you summarize each of these to someone who is not familiar with each of these functions?

Answer 1

a)probability mass function:

it is a frequency function used to represent probabilities of discrete random variables (the set of discrete values may be finite or infinite)

let X is a discrete random variable with values {x₁,x_{2,...............}x_k}

P(X=x_i) ( in Y-axis) is plotted against x_i( in X-axis)

f(x)=0.12*e^x here x is discrete set of values like{0,1,2,3,4,,,,,,,,,,,,,}and f(x) is probability mass function

this is probability mass function

b)probability density function

it is a frequency function used to represent probabilities of continuous random variables (it takes all values example:real number scale)

let X is a continuous random variable whose values belongs to real number set X belongs to R{real number set}

Example:

f(x)=0.12*e^x here x is continuous and f(x) is probability density function

c) CDF :cumulative distribution function

F(x): cumulative distribution function

F(x)= f(X<=x) in case of probality mass function, F(x)=P(X=x_n) for all x_n<=x

F(x)= f(X<x) in case of probablity density function, F(x)=P(x)dx limits(lower=-infinity, upper=x)

the maximum value of CDF is 1

the area under the curves PDF and PMF is equal to 1