### Questions (12)

 4 Recurrence relation for the number of strings of length $n$ over the alphabet $\{1, 2,3,4,5,6,7\}$ such that there are no consecutive $1$'s or $2$'s. 2 Foster's Theorem for Recurrence in Markov Chains 2 Number of integer solutions to $S_{1}+S_{2}+S_{3}+S_{4}+S_{5}+S_{6} = 30$ with constraints 2 if $X\sim \operatorname{Bin}(n,p)$ and $Y={X \choose 2 }$ What is the intuition behind $E(Y) = {n \choose 2}p^2$ 2 Limit of $\lim_{n\to\infty}n\cdot \sqrt[n]{\sin\left(\frac{1}{1}\right)\cdot \sin\left(\frac{1}{2}\right)\cdots\sin\left(\frac{1}{n}\right)}$

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 2 Recurrence relation for the number of strings of length $n$ over the alphabet $\{1, 2,3,4,5,6,7\}$ such that there are no consecutive $1$'s or $2$'s. 0 How can a stopping time be independent of its stochastic process?

### Tags (31)

 2 combinatorics × 4 0 limits × 2 0 real-analysis × 4 0 probability × 2 0 calculus × 3 0 probability-distributions 0 sequences-and-series × 2 0 radicals 0 stochastic-processes × 2 0 random

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