**Cumulative density function**- CDF is summation of all the probabilities within a range. The CDF is the integral of the PDF (Probability density function).

Read Jack Lion Heart's answer to What is the difference between a probability density function and a cumulative distribution function? on Quora

- “d” - returns the height of the probability density function
- “p” - returns the cumulative density function
- “q” - returns the inverse cumulative density function (quantiles)
- “r” - returns randomly generated numbers

**R Examples**

pnorm(700,500,100)

Mean - 500

Variance - 100

This score 700 is better than 97% of other scores

v <- c(-1,1,2)

dnorm(v)

plot(v,dnorm(v))

plot(v,pnorm(v))

dnorm(0,mean(v),sd(v))

Link Ref

**Normal distribution**is defined by the following probability density function, where μ is the population mean and σ2 is the variance.

**Chi-squared Distribution**- If X1,X2,…,Xm are m independent random variables having the standard normal distribution, then the following quantity follows a Chi-Squared distribution with m degrees of freedom

**Binormial Distribution**- binomial distribution is a discrete probability distribution. It describes the outcome of n independent trials in an experiment.

**Two Extra Parameters**- number of trials and the probability of success for a single trial

__Distribution function__
x <- seq(0,50,by=1)

y <- dbinom(x,50,0.2)

plot(x,y)

50 - Number of Trials

0.2 - Probability of success for each trial

__Cumulative Probability Density Function__
x <- seq(0,50,by=1)

y <- pbinom(x,50,0.5)

plot(x,y)

50 - Number of Trials

0.5 - Probability of success for each trial

**Random Probability Density Function**
x <- seq(0,50,by=1)

y <- rbinom(x,50,0.5)

plot(x,y)

**Happy Learning, More Learning Needed...It's vast....Lot more efforts needed :)**