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# R - Binomial Distribution

The binomial distribution model deals with finding the probability of success of an event which has only two possible outcomes in a series of experiments. For example, tossing of a coin always gives a head or a tail. The probability of finding exactly 3 heads in tossing a coin repeatedly for 10 times is estimated during the binomial distribution.
R has four in-built functions to generate binomial distribution. They are described below.
```dbinom(x, size, prob)
pbinom(x, size, prob)
qbinom(p, size, prob)
rbinom(n, size, prob)
```
Following is the description of the parameters used −
• x is a vector of numbers.
• p is a vector of probabilities.
• n is number of observations.
• size is the number of trials.
• prob is the probability of success of each trial.

## dbinom()

This function gives the probability density distribution at each point.
```# Create a sample of 50 numbers which are incremented by 1.
x <- seq(0,50,by = 1)

# Create the binomial distribution.
y <- dbinom(x,50,0.5)

# Give the chart file a name.
png(file = "dbinom.png")

# Plot the graph for this sample.
plot(x,y)

# Save the file.
dev.off()
```
When we execute the above code, it produces the following result −

## pbinom()

This function gives the cumulative probability of an event. It is a single value representing the probability.
```# Probability of getting 26 or less heads from a 51 tosses of a coin.
x <- pbinom(26,51,0.5)

print(x)
```
When we execute the above code, it produces the following result −
```[1] 0.610116
```

## qbinom()

This function takes the probability value and gives a number whose cumulative value matches the probability value.
```# How many heads will have a probability of 0.25 will come out when a coin is tossed 51 times.
x <- qbinom(0.25,51,1/2)

print(x)
```
When we execute the above code, it produces the following result −
```[1] 23
```

## rbinom()

This function generates required number of random values of given probability from a given sample.
```# Find 8 random values from a sample of 150 with probability of 0.4.
x <- rbinom(8,150,.4)

print(x)
```
When we execute the above code, it produces the following result −
`[1] 58 61 59 66 55 60 61 67`

1. R - Overview
2. R - Environment Setup
3. R - Basic Syntax
4. R - Data Types
5. R - Variables
6. R - Operators
7. R - Decision Making
8. R - Loops
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18. R - CSV Files
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31. R - Mean, Median and Mode
32. R - Linear Regression
33. R - Multiple Regression
34. R - Logistic Regression
35. R - Normal Distribution
36. R - Binomial Distribution
37. R - Poisson Regression
38. R - Analysis of Covariance
39. R - Time Series Analysis
40. R - Nonlinear Least Square
41. R - Decision Tree
42. R - Random Forest
43. R - Survival Analysis
44. R - Chi Square Tests