Tagged Questions
0
votes
0answers
42 views
A question on the exponential distribution [closed]
I am wondering if you could help me with the following:
Charlie and Bella and their friends Mark and Leonard each have a toy. Each toy breaks at a time that is exponentially distributed with ...
1
vote
0answers
31 views
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 ...
2
votes
1answer
65 views
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, ...
-2
votes
1answer
53 views
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.
0
votes
2answers
69 views
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 ...
0
votes
1answer
87 views
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 $σ_1^2$. ...
3
votes
0answers
44 views
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 ...
1
vote
1answer
55 views
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 ...
0
votes
2answers
79 views
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 ...
-1
votes
1answer
26 views
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. ...
1
vote
0answers
58 views
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 ...
-1
votes
1answer
92 views
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 ...
2
votes
0answers
64 views
How to show independence and interpret the result
If $X$ is symmetrically distributed about zero , then show that $U=|X|$ and
$$V = \left\{
\begin{array}{}
+1, & X \geq0 \\
-1, & X<0
\end{array}
...
1
vote
1answer
79 views
Find the limiting distribution of $Z_n$
Let $X_1,X_2, \dots$ be iid RVs with mean $\alpha$ and variance $\sigma^2$ , and let $Y_1,Y_2, \dots$ be iid RVs with mean $\beta(\neq 0)$ and variance $\tau^2$. Find the limiting distribution of ...
0
votes
0answers
40 views
Distribution of transformation
Suppose $X_1,\ldots,X_n$ are i.i.d. $\mathcal U(0,1)$. I am looking for the asymptotic distribution of $$T_n = \prod_{i=1}^n [e{X_i}]^{1/\sqrt{n}} \>.$$
3
votes
1answer
178 views
Sum of Binomial and Poisson random variables
If we have two independent random variables $X_1 \sim \mathrm{Binom}(n,p)$ and $X_2 \sim \mathrm{Pois}(\lambda)$, what is the probability mass function of $X_1 + X_2$?
NB This is not homework for ...
1
vote
0answers
30 views
Sampling distributions help with questions [duplicate]
Possible Duplicate:
Probability of mean of random sample being in a certain range
When a pizza restaurant’s delivery process is operating effectively, pizzas are delivered in an average of ...
0
votes
0answers
91 views
Deriving asymptotic distribution
I'm working on a question and I appreciate if you could guide me on how to approach it. Here is the question:
Consider $Y_1, Y_2, \ldots, Y_n$ as iid with density $f(y;\theta)$ and assume that the ...
3
votes
0answers
158 views
Simple question Maximum Likelihood
I have the following distribution, defined for $0 < x < \theta$, its value is $0$ otherwise.
$$f_\theta(x)= \frac{2x}{\theta^2} $$
Find the MLE of $\theta$
I tried:
$$\prod_{i=1}^n ...
1
vote
1answer
149 views
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 ...
3
votes
1answer
106 views
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):
...
5
votes
1answer
67 views
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 ...
2
votes
0answers
120 views
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 ...
3
votes
0answers
191 views
What is the distribution of the ratio of sums of squared normal random variables?
Given that $Y_1, \ldots, Y_6$ are independent normal random variables with mean $0$ and variance $\sigma^2$. Find the distribution of the following
$ ...
0
votes
1answer
110 views
How to find distribution of some statistics for i.i.d. normal random variables?
Let $Y=(Y_1,Y_2,\ldots,Y_n)^{T}$ and $Y_1,\ldots,Y_n$ are independent normal random variables with mean $0$ and variance $ \sigma^2$. Find the distribution of the following statistics and give your ...
1
vote
2answers
350 views
Let the random point (X,Y) be uniformly distributed on the square
Let the random point $(X,Y)$ be uniformly distributed on the square
$D=\{(x,y):-1\leq x\leq 1,\ -1\leq y \leq 1\}$.
Find the distribution function and the probability distribution function of $Z=X ...
5
votes
1answer
594 views
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 ...
-3
votes
1answer
166 views
Pairwise vs. total independence of discrete uniform random deviates
Let $X$ be a discrete uniform random variable on the set $\{000, 011, 101, 110\}$ of four binary integers, and let $X_{i}$ denote the ith digit of $X$, for $i = 1, 2, 3$. Show that $X_{1}, X_{2}, ...
3
votes
1answer
801 views
Weibull moment generating function and Gamma function
I'd be grateful for any hints or help with this question:
Let $X$ follow the Weibull distribution with pdf
$f(x)=\beta x^{\beta-1}e^{-x^{\beta}}$
on $x>0$ with $\beta>0$. Show that
...
-1
votes
0answers
117 views
How to solve/compute for normal distribution and log-normal CDF inverse? [duplicate]
Possible Duplicate:
Calculating percentile of normal distribution
Edit: I think the hint is Box-Muller transformation. Any ideas?
I am trying to find the inverse of normal CDF.
This is ...
0
votes
1answer
113 views
Evaluating probability mass function for a discrete random variable
Consider the following pmf for a discrete random variable $X$: $f(x) = x/15$ when $x = 1, 2, 3, 4, 5$, and $f(x)= 0$ for all other values of $x$. What is $f(3)$? (I.e., the PMF evaluated at 3)
1
vote
3answers
86 views
I know the probability of an outcome in a sample, how to apply to population?
I admittedly am horrible at statistics. I know that the probability of an individual who has saved for retirement has saved less then 50,000 USD is 16.4% according to my sample data, but only 69% of ...
2
votes
1answer
83 views
Simple relative frequency calculation, confusing wording
I am admittedly doing homework, but two problems are worded in such a way that is confusing me. Part (b) asks, "Determine the probability that an individual who has saved for retirement has saved less ...
3
votes
1answer
968 views
Distribution of a ratio of uniforms: What is wrong?
Suppose that $X$ and $Y$ are two i.i.d. uniform random variables on the interval $[0,1]$
Let $Z=X/Y$, I am finding the cdf of $Z$, i.e. $ \Pr(Z\leq z) $.
Now, I came up with two ways of doing this. ...
3
votes
2answers
665 views
How to find a marginal distribution from a joint distribution?
So I have this joint dist
$$f(x,y) = \frac{1}{2\pi}\exp(-\frac{x^2}{2} - \frac{y^2}{2} + x^2y - \frac{x^4}{2})$$
I'd like to find $f_x(x)$. So I know that means I need to integrate function wrt y. ...
0
votes
0answers
147 views
Sampling distribution [editted] [closed]
With a given mean , standart deviation, How can one determine the mean and the sampling distribution of the sample mean for a*random* sample of size n ( n is known and, of course it is an national ...
8
votes
2answers
486 views
What kind of distribution is $f_X(x) = 2 \lambda \pi x e^{-\lambda \pi x ^2}$?
What kind of function is:
$f_X(x) = 2 \lambda \pi x e^{-\lambda \pi x ^2}$
Is this a common distribution? I am trying to find a confidence interval of $\lambda$ using the estimator ...
4
votes
2answers
446 views
Uniform random variable distribution
This is a homework problem out of the book. It says
If $U$ is a uniform random variable on [0,1], what is the distribution of the random variable $X = [nU]$, where [$t$] denotes the greatest ...
0
votes
1answer
1k views
Difference between sampling distribution and data distribution
I went to a stats course refresher last week and the instructor talked about data distribution and sampling distribution. I am just practicing with the exercises shown in class.
Based on my dataset ...
0
votes
0answers
112 views
Help with homework with Normal distribution [closed]
Please help me with the following questions.
If x is normally distributed with population mean 100 and standard deviation 8, find
p(x < 107)
p(x < 100)
p(103 < x < 114)
Find the ...
0
votes
0answers
265 views
How to calculate probability for a multivariate/continuous event
I'm brushing up my stats for an AI course that is going to show me the Gaussian mixture model. My prof said I'm supposed to know how to "calculate the probability of a multivariate and continuous ...
2
votes
2answers
2k views
Proving that the squares of normal rv's is Chi-square distributed
I start with three independent random variables, $X_1, X_2, X_3$. They are each normally distributed with:
$$X_i \sim N(\mu_i, \sigma^2), i = 1, 2, 3.$$
I then have three transformations,
...
0
votes
1answer
97 views
Probability and limits
I've been having some trouble with this story problem. Any help you could give me would be really appreciated.
A store manager monitors the store's temperature by taking 4 independent temperature ...
4
votes
1answer
169 views
Factorization of a joint density over a directed graph
Let $G = (V,E)$ be a directed acyclic graph.
Let $i \rightarrow j$ be an edge such that the parents of $j$ are exactly:
the parents of $i$,
and $i$.
Let $L\left(G \right)$ be the set defined ...
2
votes
1answer
923 views
Regression Proof that the point of averages (x,y) lies on the estimated regression line
How do you show that the point of averages (x,y) lies on the estimated regression line?
