# Questions tagged [normal-approximation]

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1answer
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### Can Student's t-distribution be used in Normal Approximation to Binomial?

The question nearly covers it all. I clearly have a binomial distribution, however the variance and standarddeviations are unknown, the population is also just ...
1answer
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### Central Limit Theorem Approximation and Relation to Law of Large Numbers

Assume the Linberg-Levy CLT to where we know $$\sqrt{n}\frac{\bar{X}_n-\mu}{\sigma}\xrightarrow{d}N(0,1).$$ I feel like I commonly see then that $$\bar{X}_n\approx N(\mu,\frac{\sigma^2}{n}),$$ but ...
1answer
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1answer
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### Lower Bound on the Total Variation Distance between two Binomials

Let $X= B(n,1/2)$, $Y=B(n,1/2 + \delta)$, for a small $\delta >0$ be two Binomial Distributions. Question 1. I am looking for a lower bound on the Total Variation Distance the two Binomials ...
2answers
143 views

### A box contains 48 tickets  and 52 . If you draw 10 times at random and with replacement, what is the probability of getting a sum of 3 or less?

I came across a question like this and I try it to solve it by 2 different methods. However, these 2 methods don't yield the same answer. So, I'd like to ask you what am I missing. I'm clearly doing ...
0answers
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### How to test proportion against 1 - null hypothesis: H0: p=1

My research question: I have a data set with good observations and bad observations and have to estimate if all observations are good in the population with 99% confidence. My suggested method: My ...
1answer
93 views

### Approximate meaning of probability? [closed]

After the football match each football fan leave on the stadium 2 empty bottles. The janitor finds the bottle with probability 0.3. Find the approximate meaning of probability that the janitor ...
0answers
138 views

### Bayesian inference via approximate data likelihood

Suppose that we have a very large i.i.d. sample $x_1,...,x_n$ and a data likelihood defined by $$p(x | \theta,\beta) = \prod_ip(x_i | \theta,\beta)$$. Further suppose that $\theta$ is the parameter ...
1answer
260 views