Question

1. Let X be a discrete random variable with a cumulative distribution function:

$P(X\leq x) = 1 -(1-p)^x, \;x\geq 0$

a. Use this cdf to fin the limiting distribution $P(X_n\leq x)$ of the random variable$X_n=\frac{X}{n}$ when

$p=$ with $\lambda>0$, as n increases.

Use the fact $x\in \mathds{R}, lim_{n\rightarrow \infty}(1+x/n)^n=e^x$

b. What kind of random variable is $X_n$ for large value of n?

p=

Answer 1

Cai wen 20. rn)