### 8.4.14 The exponential distribution

#### The probability density function for the exponential distribution: exponential exponentiald

The exponential distribution depends on one parameters, λ>0; the value of the density function at x ≥ 0 is exponential(λ,x) = λ e−λ x. If you enter

exponential(2.1,3.5)

for example, you will get

0.00134944395675

#### The cumulative distribution function for the exponential distribution: exponential_cdf exponentiald_cdf

The cumulative distribution function for the exponential distribution with parameter λ > 0 at a value x ≥ 0 is exponential_cdf(λ,x) = Prob(X ≤ x). If you enter

exponential_cdf(2.3,3.2)

for example, you will get

0.99936380154

If you give exponential_cdf an extra argument y > x, you will get the probability that the random variable lies between the two values; exponential_cdf(λ,x,y) = Prob(x ≤ X ≤ y). If you enter

exponential_cdf(2.3,0.9,3.2)

you will get

0.125549583246

#### The inverse distribution function for the exponential distribution: exponential_icdf exponentiald_icdf

The inverse distribution function for the exponential distribution with parameter λ > 0 is computed with exponential_icdf(λ,h); recall that this will return the value x with exponential_cdf(λ,x) = h. If you enter

exponential_icdf(2.3,0.87)

you will get

0.887052534142