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(Solved): 3. Fix p(0,1) and let (Xn)n=1 be a sequence of random variables where XnNb(n,p) f ...

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3. Fix

p \in (0, 1)

and let

(X_{n})_{n = 1}^{\infty}

be a sequence of random variables where

X_{n} \sim N b (n, p)

for all

n \geq 1

. Use the Weak Law of Large Numbers to show that

\frac{X _{n}}{n} \to p \frac{1}{p}

.

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