# Bernoulli distribution with non integer number of trials

Can we generalise the Binomial distribution for a non-integer number of Bernoulli trials?

• How do you imagine a 4.5th trial for example?
– Alex
Apr 20, 2016 at 12:48
• I am not entirely confident in my answer, since I am still wrapping my head around this thing. Let's say that the binomial will give us the value of X where $X+c < 11$. Now, assume that we know that c = 5.5 Apr 20, 2016 at 12:58

a) either by considering the natural generalization of (discrete) Binomial Distribution B(n,p) into (continuous) Normal distribution, with pdf $$\dfrac{1}{\sigma \sqrt{2 \pi}}e^{-(x-np)^2/(2 \sigma^2)}$$ with $$\sigma^2=npq$$ and taking $$n=9/2$$ for example.
b) or, if one desires to stay with discrete random variables, define (artificially!!!) $$X \sim Bin(4.5,p)$$, by taking $$X=Y/2$$ with $$Y \sim Bin(9,p)$$.
• I see, you really killed it with the infinite divisibility concept. There is not answer to my problem looks like. Out of curiosity, how would you handle the following. Let's say that the binomial will give us the value of X where $X+c<11$. Now, assume that we know that c = 5.5 Apr 20, 2016 at 13:32