- #1
mnb96
- 715
- 5
Hello,
I considered a Binomial distribution B(n,p), and a discrete random variable [tex]X=\frac{1}{n}B(n,p)[/tex]. I tried to compute the characteristic function of X and got the following:
[tex]\phi_X(\theta)=E[e^{i\frac{\theta}{n}X}]=(1-p+pe^{i\theta/n})^n[/tex]
I tried to compute the limit for [itex]n\to +\infty[/itex] and I got the following result:
[tex]\lim_{n\to\infty}\phi_X(\theta)=e^{ip\theta}[/tex]
How should I interpret this result?
That characteristic function would correspond to a delta-function distribution centered at -p. It doesn't make much sense to me.
I considered a Binomial distribution B(n,p), and a discrete random variable [tex]X=\frac{1}{n}B(n,p)[/tex]. I tried to compute the characteristic function of X and got the following:
[tex]\phi_X(\theta)=E[e^{i\frac{\theta}{n}X}]=(1-p+pe^{i\theta/n})^n[/tex]
I tried to compute the limit for [itex]n\to +\infty[/itex] and I got the following result:
[tex]\lim_{n\to\infty}\phi_X(\theta)=e^{ip\theta}[/tex]
How should I interpret this result?
That characteristic function would correspond to a delta-function distribution centered at -p. It doesn't make much sense to me.
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