# Tagged Questions

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### How to test whether the distribution of majors among grad students differ from that of incoming students?

A university offers degrees in the following areas: Arts/Science Engineering Business Computer Science Incoming freshmen apply for majors in Arts, Science, Engineering, Business, and Computer ...
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### Probability and Sampling distribution

Would you please explain me the difference between Probability distribution and Sampling distribution easily ? Is that the difference : in probability distribution we have probability for every ...
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### Posterior distribution of the parameter knowing the prior

I have exponentially distributed probability of event $E$ $$P(E|a) = a \exp(-aE),$$ where $a$ is the rate parameter of the exponential distribution. Now the probability distribution for $a$ is a ...
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### In regression, which distribution will have the largest standard deviation?

the predicted scores on the outcome variable, Ŷ the residuals the observed scores on the outcome variable, Y the standardized regression coefficients My understanding is that the question wants ...
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### Beyond the normal distribution: what if a particular distribution can't be assumed

In a random sample of 150 community college students, the mean number of hours spent studying per week is 11.7 hours and the standard deviation is 4 hours. Without assuming anything about the ...
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### Find the Distribution

Given $Y_1, Y_2..Y_n$ are iid from a distribution with pmf, $f(y) = a^{2}$ for $y=0$, $f(y) = 2a(1-a)$ for $y=1$ , $f(y) = (1-a)^{2}$ for $y=2$, where $0<a<1$. For large n, calculate the ...
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### How to get exact distribution of estimated p for binomial distribution?

This question is kind of a follow up of another question I had: Asymptotic normal distribution via the central limit theorem There I had to calculate the estimator for $p$ (meaning $p$ for success) ...
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### How to compute expectations from a probability density function?

How to find a tax/subsidy in an income probability density function situation? I am asked the following question: Suppose all families with $Y \lt 20$ are given transfer payments equal to ...
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### Method to determine distribution of data

Is there a book or paper which mentions the ways how to find the distribution of observed signals. After the mean and variance is found out, how do I determine/find the distribution to which it ...
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### What distribution does “arrival of people” at an event in time follow?

Suppose that there is a Cricket match scheduled on Sunday, this weekend. We know that people do not arrive at the stadium at constant rate. Few hours before scheduled start of the match, people start ...
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### Given a mean and standard deviation, what can you determine of a non-normal distribution?

I have the following question: Given a mean of 11 and a standard deviation of 2, with a non-normal distribution, can you determine the % of numbers that are between 8 and 12? My guess is ...
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### Convergence in distribution and limiting distribution

I'm trying to solve the problem below: Let $X_1,...,X_n$ be independent with PDF $f(x)=e^{-x}$ if $x>0$ and zero otherwise and define $$X_{(n)} = \mathrm{max}\{X_1,..,X_n\}$$ Find the CDF of ...
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### UMP test for one-sided hypotheses

Is it possible to identify a UMP test for one-sided hypotheses on $\theta$  for the case of an i.i.d. sample $(X_1, ..., X_n)$ of random variables $X_i \sim f_\theta (.)$ such that the ...
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### Finding a sufficient statistic

Consider an i.i.d. sample $(X_{1},\ldots, X_{n})$ where the $X_{i}$ have density $f(x) = k \cdot \exp(−(x − θ)^4)$ with $x$ and $\theta$ real, obtain the sufficient statistic and its dimension. What ...
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### Use of Weibull model or Weibull distribution

I have a basic question regarding use of the terms "Weibull model" and "Weibull distribution". (I take Weibull as an example, but the question could apply to any distribution.) I read in books or ...
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### Difficulty in calculating joint probability

I have a table. ...
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### Two dice problem

Two players are throwing each one die. The one that has higher value, receives a number of points equal to the difference of the values on both dice. How do you estimate probability for a winner to ...
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### Jaccard Similarity - From Data Mining book - Home work problem.

Exercise 3.1.3 : Suppose we have a universal set U of n elements, and we choose two subsets S and T at random, each with m of the n elements. What is the expected value of the Jaccard similarity of ...
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### The meaning of translation completeness w.r.t a random variable

I stumbled upon this term in McFadden - Analysis of qualitative choice behavior (page 111). It is said that "A random Variable $X$ is translation complete if for a function h of bounded ...
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### Joint distributions for uncorrelated varibles

Can someone think of joint distribution of random variables X, Y such that the following three conditions are satisfied: $E[X] = 1$, $E[Y] = 1$, and $E[XY] = 0$? A friend of mine asked me this, ...
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### What is the sample standard error formula?

What is the sample standard error formula? I know only $s$ but I guess this is not it. I am confused about its formula. Please help me. Thank you.
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### Simple homework question about normally distributed variables

The question states: Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$. What is ...
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### How to derive a confidence interval from an F distribution?

So, this is the question I'm working on: Suppose we observe a random sample of five measurements: 10, 13, 15, 15, 17, from a normal distribution with unknown mean $µ_1$ and unknown variance $σ_1^2$. ...
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### Likelihood analysis for exponential distribution

Assume a collection of independent exponential random variables $y_{1}, \ldots, y_{n}$ with means $\mu_{1}, \ldots, \mu_{n}$; where $\mu_{i} = \beta_{0}+\beta_{1}x_{i}$. How can I find the profile ...
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### Use the Central Limit Theorem to calculate the approx probabilities of Gamma RVs?

If $X_i, i=1,...,$ are independent, identically distributed $\operatorname{N}(0,1)$ random variables, and $Y_i = X_i^2$ are independent $\operatorname{Gamma}(\frac{1}{2},\frac{1}{2})$ RVs, use the ...
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### Normal approximation to binomial

What do I do when the normal approximation is not valid? Here's the question I'm trying to answer: A student guesses all 15 answers on a multiple-choice test. There are 5 choices for each of the ...
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### what are the dependent and independent factors and categorical for below project [closed]

my project is identification of factors influencing motor bikes for home to office trip. there are some attiributes like gender,age,marital status,education qualification,job type,working sector, no. ...
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### Distributions of $X+Y$,$X-Y$,$XY$ for $(X,Y)$ Chosen Uniformly Inside Triangle [closed]

Let $(X,Y)$ be chosen uniformly on the triangle $\{(x,y)\in\mathbb R^2:x+y\leq1,x\geq0,y\geq0\}$. What is the density function of $(X,Y)$? Find the distributions of $X+Y$, $X-Y$,$XY$. What I've ...
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### Plot the binomial distribution

How to plot the binomial distribution for p = 0.3, p = 0.5 and p = 0.7 and the total number of trials n = 60 as a function of k the number of successful trials. For each value of p, determine 1st ...
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### If MGF exists, does it imply that all $E(X^n)$ exist? [duplicate]

Possible Duplicate: Existence of the moment generating function and variance Given that there is an interval $-h < t < h$ where MGF exists, does it imply that the distribution's ...
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### How to understand the data of company's revenues

I'm taking a first course in statistics. I have been given a dataset with the number of companies falling into different categories of revenues (in thousands of euros): ...
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### If $Y \sim geometric(P)$ and $P \sim \mathcal B(2, 1)$ how to compute $E(Y)$ and marginal pmf of $Y$?

$$Y \sim Geometric(P)\\ P \sim \mathcal B(2, 1)$$ I'm trying to compute $E[Y]$ without finding marginal distribution of $Y$. I need some hints here. I also need to find the pmf of $Y$. My approach ...
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### If $X \sim {\rm Bernoulli}(p)$, what is the distribution of $Y=aX-b$?

Let $X \sim {\rm Bernoulli}(p)$ and $Y=aX-b$. I want to find the distribution of $Y$. I am assigned a homework problem with specific $a$ and $b$. My textbook covers methods for solving this, given ...
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### How to show that polar coordinates in a uniform distribution on a disk are independent?

Let the random point $(X,Y)$ be uniformly distributed on the unit disc $D=\{(x,y):x^{2}+y^{2}<1\}$. Show that the polar coordinates $R\in [0,1)$ and $\theta \in [0,2\pi)$ of the point are ...