What is the probability of getting the value of random variable exactly equal to r?

[faryal]

The commulative density function CDF of Rayleigh is given by:
Pr(r ≤R)=1-exp(-R^2/2σ^2)
What is the probability of getting the value of random variable exactly equal to r?

 

[dick_freebird]

-Exactly-? That's zero. The smaller your bucket, the
less you catch.

Within some tolerance, goes like tolerance/span but of
course details of distribution and position relative to
mode matter.

 

[faryal]

-Exactly-? That's zero. The smaller your bucket, the
less you catch.

Within some tolerance, goes like tolerance/span but of
course details of distribution and position relative to
mode matter.

i didn't understand your answer, kindly elaborate

 

[crutschow]

It's related to the resolution of your calculations. "Exactly" means infinite resolution (infinite number of zeros after the decimal point) which is not possible in practice. So you need to decide the resolution of your calculations, which will determine the width of your sample (which basically ±0.5 of the least significant digit) and thus the probability of a sample being at that value.