# Tagged Questions

For question about limit theorems of probability theory, like the law of large numbers, central limit theorem or the law of iterated logarithm.

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### Asymptotic Relative Efficiency: Poisson

I'm trying to find the asymptotic relative efficiency of a Poisson process: $$\frac{\lambda^t \exp(-\lambda)}{t!} = P(X=t).$$ When $X = t = 0$, the best unbiased estimator of $e^{-\lambda}$ is ...
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### Compute imaginary part of the limit

I am trying to compute the imaginary part of this particular question $$\lim_{z\rightarrow i} \frac{iz^3}{z+9 i}$$
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### Find $\alpha$ such that $\lim_{(x, y) \to (0, 0)} \frac{|x|^\alpha y}{x^2 + y^2} = 0$. Can I simply move to polar coordinates?

This is the full exercise: Given function: $$f(x, y) = \begin{cases} \frac{|x|^\alpha y}{x^2 + y^2}, & \text{if }(x,y) \ne (0, 0) \\ 0, & \text{if } (x,y) = (0,0) \\ \end{cases}$$ ...
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### Is $\lim_{n\rightarrow\infty }nz^{n!n}=0$ for $|z|<1$?

Is $\lim_{n\rightarrow\infty }nz^{n!n}=0$ for $|z|<1$? We have a $\infty \cdot 0$ case, then how we proceed? How to use the L'Hospital's Rule? Thanks in advance!
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### determine the limit of sequence?

Need help on how to determine the limits, if it exists for this sequence. Have no idea where to start. Thanks in advance smart people! $$A_n = \dfrac {(n+2)^{2n}}{(n^2-n-6)^n}$$
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### how to find existence and value of limit in multivariable calculus

I was in maths class and i found a question interesting. Find the limit of $\lim_{(x,y)\to (0,0)} \frac{2x}{x^2+x+y^2}$ if it exist.one of my friend did this question by transforming into polar ...
I was asked to find the limit of the following: $$\lim_{x\to -1}\frac{\sqrt {x ^ 2 + 8} - 3}{x + 1}$$ I have tried using the Limit Laws but am always getting $\frac {0}{0}$. The answer given is ...