The correctness of EvalExponentialPdf method in thinkbayes2.py

[18fanfan]

Dear professor Downey,

In chapter 7.6, you would like to compute the time between goals and the code in EvalExponentialPdf method is:

return lam*math.exp(-lam*x)

but I think the probability between two events is:

return math.exp(-lam*x)

The first term lam variable should be dropped.

Here comes my justification: Assume T is the time interval between two goals. The Pr(T > x ) means the probability in a certain time interval x should not occur scoring. so we take the k=0 to the Poisson distribution, then we got math.exp(-lam*x).

Although I know the EvalExponentialPdf only be called by MakeExponentialPmf, and the lam variable will be canceled out after Normalize function. so the result stays the same. But I still want to confirm with you the correctness of the method. Thanks in advance!

[AllenDowney]

I believe the function EvalExponentialPdf correctly computes the PDF of the exponential distribution. Please check https://en.wikipedia.org/wiki/Exponential_distribution and let me know if you disagree.

On Wed, May 22, 2019, at 11:42 PM, Szu-Yueh Fan wrote:

Dear professor Downey,

In chapter 7.6, you would like to compute the time between goals and the code in EvalExponentialPdf method is:

return lammath.exp(-lamx)

but I think the probability between two events is:

return math.exp(-lam*x)

The first term lam variable should be ignored

Here comes my justification: Assume T is the time interval between two goals. The Pr(T > x ) means the probability in a certain time interval x should not occur scoring. so we take the k=0 to the Poisson distribution, then we got math.exp(-lam*x).

Although I know the EvalExponentialPdf only be called by MakeExponentialPmf, and the lam variable will be canceled out after Normalize function. so the result stays the same. But I still want to confirm with you the correctness of the method. Thanks in advance!

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[18fanfan]

Dear professor Downey,

I check the wiki, and it is the right definition. I also read this article https://neurophysics.ucsd.edu/courses/physics_171/exponential.pdf to realize the relation between the Poisson and exponential distribution.

I think I misunderstood the meaning of Pr(T > x) to explain the distribution of two goals.