Problems in probability theory
Task 1
Statement
Radioactive decay process. Find the mathematical expectation of the time of the first decay event.Solution:
The mathematical expectation (or mean value) of a random variable ξ in the general caseis the number
if this Stieltjes integral) converges absolutely.
For a continuous random variable
In our case
where
in our case k=1 since we are interested in the first decay.
E and M should be understood in the same way, different textbooks just use different notation.
Where I read the theory it was M, and when I solved problems I wrote E.
Article author: Andrei Olegovich