## Description

The Cumulative Distribution Function(CDF) is the probability that a distribution function of X will take a value less than or equal to x. The CDF of a continuous random variable X is expressed as

(1)The Sage cell below calculates the CDF for the exponential distribution when $\lambda=4$ and $X<.75$.

## Sage Cell

#### Code

```
l=4
f(X)=l * exp( -l* x)
CDF=integral(f(X),x,0,.75)
CDF
```

## Options

#### CDF for Discrete Distributions

The CDF of a discrete probability distribution function is

(2)The Sage cell below calculates the CDF of the poisson distribution when $\lambda=15$ and $x<12$.

#### Code

```
lamb = 15
x=12
var('k')
f(k)=exp( -lamb) * (( lamb^k ) / ( factorial(k)))
CDF=sum(f(k) , k, 0, x)
numerical_approx(CDF)
```

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Date: 16 Oct 2018 16:54

Submitted by: James A Phillips