0
$\begingroup$

When $ λ $ is given with a given probablity of $X$, it's a simple program, where for example I can do

f[x_] := 7*Exp[-7 x]
Probability[x > 2, x ≈ ExponentialDistribution[7]] // N 

but what if $X$ is exponentially distributed random variable with some parameter $ λ $. How would you find possible values of $ λ $, if you are only given the probability with its range of $X$ and its probability of getting these ranges $(eg: Pr(0.2≤X≤1.7) = 0.14 )$

$\endgroup$
4
$\begingroup$

Just use λ instead of 7 in your Probability expression, and solve:

Solve[
    Probability[.2 ≤ x ≤ 1.7, Distributed[x, ExponentialDistribution[λ]]] == .14,
    λ,
    Reals
]

Solve::ratnz: Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result.

{{λ -> 0.102807}, {λ -> 9.83056}}

$\endgroup$
  • $\begingroup$ NSolve works best $\endgroup$ – mastud89 Apr 11 '18 at 3:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.