Tagged Questions

The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

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Likelihood Function for the Uniform Density.

Let the random variable $X$ have a uniform density given by $$f(x;\theta)=I_{[\theta-\frac{1}{2},\theta+\frac{1}{2}]}$$ where $-\infty\leq\theta\leq\infty$ the likelihood function for a sample of ...
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Finding P value

I have these observations $(2,3.2,3.8,2.5,3.3,2.8,3.0,3.4)$ from $X \sim N(\mu,\sigma^2)$ and i want to calculate the $P$-value testing $H_0: \mu =3.2$ against $H_1 \neq 3.2$ with $\sigma = 0.6$ ...
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Identifying joint distribution

Let $Y_1$ and $Y_2$ be independent random variables with $Y_1\sim N(1,3)$ and $Y_2 \sim N(2,5).$ If $W_1=Y_1+2Y_2$ and $W_2=4Y_1-Y_2$ what is the joint distribution of $W_1$ and $W_2$? Is ...
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Maximum Likelihood Estimator of parameters of multinomial distribution

Suppose that 50 measuring scales made by a machine are selected at random from the production of the machine and their lengths and widths are measured. It was found that 45 had both measurements ...
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Likelihood Function for the Uniform Density $(\theta, \theta+1)$

Let the random variable X have a uniform density given by $f(x;\theta)$~$R(\theta,\theta+1)$ What is the maximum likelihood function according to the samples $X_1,\ldots,X_n$? The question is much ...
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Reference request, statistical inference

Good morning, I'm looking for a good reference for study on statistical inference, the main topics that will study are Tests of Hypotheses Interval estimation I recommend taking a look at Mood ...
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Likelihood Functon.

$n$ random variables or a random sample of size $n$ $\quad X_1,X_2,\ldots,X_n$ assume a particular value $\quad x_1,x_2,\ldots,x_n$ . What does it mean? The set $\quad x_1,x_2,\ldots,x_n$ ...
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Show $\psi$ and $\Delta$ are identifiable

Let $X_1$,...,$X_m$ be i.i.d. F, $Y_1$,...,$Y_n$ be i.i.d. G, where model {(F,G)} is described by $\hspace{20mm}$ $\psi$($X_1$) = $Z_1$, $\psi$($Y_1$)=$Z'_1$ + $\Delta$, where $\psi$ is an unknown ...
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Big Balloon Game

The problem In this game, you are given empty balloons one by one, and for each balloon you are to inflate it with air until you are satisfied. If it does not burst, you gain happiness points ...
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Distribution of Sum of Discrete Uniform Random Variables

I just had a quick question that I hope someone can answer. Does anyone know what the distribution of the sum of discrete uniform random variables is? Is it a normal distribution? Thanks!
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I am running a series of experiments that I expect to have similar outcomes. What is the best method to measure statistical significance?

Following on from this comment on an answer to my previous question, I'd like to know two things: what the best statistical test I can use to measure significance on the experiments I'm running? (...
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Determining the degree of freedom for a $\chi$-squared test
I have read that the degree of freedom is calculated by subtracting $1$ from the number of states a random variable can be in. I am performing a goodness of fit test on a $64\times 32$ matrix where ...