# Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

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### How to find the probability of a specific draw from the urns?

There are 3 urns each containing 10 balls whose colors are either blue or red. In an experiment a ball is drawn from the first urn. If its color is red a second ball is drawn from the second urn. And ...
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### P(A or B) given that they are dependent events

Given that an event will occur on the first trial is p and that it will occur in the second trial if it doesn't occur on the first trial is q, what is the probability that the event will occur once? ...
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### Tricky probability

The exact problem statement: A car trader usually sells 70% of cars during the last four months of the year and 50% of cars during other months. The car trades are independent and identically ...
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### Looking for a bijective transformation of gamma distributed variable such that $ga(\alpha,\beta)$ is transformed to $ga(r,\beta ')$ where $r\in(0,1)$

I have managed to derive the gamma distribution as the sum of $n$ exponentially distributed random variables, ie, $$\sum_{i=1}^n X_i \sim Ga(n,\beta=1/\lambda)$$ where each $X_i \sim Exp(\lambda)$. ...
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### The limiting distribution of MLE is chi-squared

I have a ML estimator . How can show that the limited distribution of this ML estimator is chi-squared? Thanks very much.
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### How to solve this Categorical Data Analysis problem? [closed]

In murder trials in 20 Florida counties during 1976 and 1977, the death penalty was given in 19 out of 151 cases in which a white killed a white, in 0 out of 9 cases in which a white killed a black, ...
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### What is the lower and upper quartil of a set of size one?

I have to implement a function to calculate inter quartil range. It should work for arbitrary lists of data. However for edge cases I am unsure how mathematicians actually define the quartil of a set. ...
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1 vote
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### sum, max and difference of dependent discrete random variables

I am trying to calculate the following random variable distribution: $Z= \sum _{i=0} ^{n} [max(X_0, X_1, X_2,...,X_n)-X_i]$ I know $X_i$ probability distribution ($X_i$ are i.i.d. random variables), I ...
1 vote
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### Gaussian Bell Curve

Is the Gaussian Bell Curve time dependent? Suppose we toss a coin and depending on the outcome we win or lose one dollar. If we do it for a long time (infinity), the outcome when plotted will resemble ...
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Im trying to study for my statistics exam and Im having trouble with this question. "Imagine you wished for 2 christmas gifts.The chance of getting J1 is 0,8. The chance of getting J2 is 0,2 if ...
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1 vote
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### Normal approximation of the ratio of Normally distributed random variables sums

Given $n$ independent Normally distributed random variables $X_i \sim N(\mu_i, \sigma^2_i)$ and $n$ real constants $a_i \in \mathbb{R}$, I need to find an acceptable Normal approximation of the ...
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### Find the distribution of Q [closed]

Let $X_1, X_2,..., X_9$ denote a sample. Assume that $X_i \sim N(4\theta, \theta^2)$ for $i = 1,...,9$ with an unknown $\theta > 0$. We want to find the confidence interval for $\theta$. a) Find ...