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
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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
for example, you will get
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
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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
you will get