**5.708 distributions questions.**

I have this statistics oriented question and I need some input on the approach. There is a new product introduced, a contact lence that has seleral ranges of attributes (powers) from which the users ...

Let X and Y be uniformly distributed on a unit disk such that
$x^2 + y^2 + 2 \leq 1$
Let $R = \sqrt{X^2 + Y^2}$. Find the CDF and PDF of $R$.
I start by writing
$P(X^2 + Y^2 \leq -1)$,
but this ...

A basketball player succeeds in making a basket three tries out of four. How many
times must he try for a basket in order to have greater than 0.99 probability of making
at least one basket?
In this ...

Given $Z_1, Z_2$ are i.i.d standard normal random variables.
Let
$$V:=\frac{Z_1}{\sqrt{(Z_1^2+Z_2^2)/2}}$$
Derive the pdf of $V$.
The numerator and denominator of $V$ are dependent, so the square ...

I have this homework question where there are 3 random variables $(U_0,U_1,U_2)$ which are independent and uniform in the interval $[-1,1]$.
I have two other random variables $(X,Y)$ defined as ...

I have this vector data and I am trying to find distribution that this data fits.
...

What is the difference between several/Multivariate Random Variables (RVs) & a Sequence of RVs?
Example: Picking a student from class and noting his/her height and weight is several RVs (...

I've been trying to prove the following:
$$\phi'(x)(1-\Phi(x))+2\phi(x)^2>0$$
where $\phi$ is the standard Normal pdf and $\Phi$ its cdf. I've tried many simulations and I believe it's true in ...

What is the probability of a 1,1 distribution in Bridge when there are 2 cards outstanding? I understand there are 4 possible outcomes, for example Kx and 0, 0 and Kx, K and x, x and K. That is, 2 ...

I was thinking about the meaning of location-scale family.
My understanding is that for every $X$ member of a location scale family with parameters $a$ location and $b$ scale, then the distribution of ...

In my notes from university I have written down that the residual standard error (from normal linear regression) has the following distribution
$\frac{\hat{\sigma}^2}{\sigma^2}\sim \frac{\chi^{2}_{n-...

I am curious what the derivation for the expectation of the maximum of two jointly normal random variables $X$ and $Y$ with correlation coefficient $\rho$.
I could start with the following but the ...

As part of a complicated project relating to widgets being sent out to incorrect factories ("missorts"), I am examining a process which involves operators standing on a conveyor belt, removing widgets ...

I am seeking an approach to sampling conditional joint distribution (new to probability). I will put my case in a simple way:
Similar question for discrete variables is asked Here but not yet ...

I'm analysing some datasets that produce heavy tailed data when plotted as a histogram. My initial goal was to attempt to fit a known distribution to my dataset. Thereafter I use to the properties of ...

Why does the Scipy Generalised Gamma distribution have 2 shape parameters when other implementations only require one. See wikipedia and R(GAMLSS) for examples.

Consider a random variable with a known distribution. I want to know if we quantized the variable the how the probability density function(PDF) would change? Specifically, if the original PDF is ...

Suppose $X_1,\ldots,X_n,Y_1,\ldots,Y_n$ are i.i.d $\mathcal N(0,1)$ random variables.
I am interested in the distribution of $$U=\frac{\sum_{i=1}^n X_iY_i}{\sum_{i=1}^n X_i^2}$$
I define $$Z=\...

In Poisson point processes, we first let $N$ be a random Poisson random variable, with parameter $\lambda$:
$$
P(N=n)=\frac{e^{-\lambda}\cdot\lambda^n}{n!},\qquad n=0,1,\ldots
$$
Without loss of ...

Let $D$ be a one-parameter distribution family whose support is the positive reals. Let $D_x$ be a distribution from this family parametrized by its mean $x \ge 0$, let $X \sim D_x$ and $Y \sim D_y$ ...

I know that the sampling distribution of the mean can be assumed to be normal if N>30, but does this have an implication on the "30" itself (the sample data)?
I have three different time series with ...

I know that if $X_1$ and $X_2$ follow a Gamma distribution with parameters $(p_1,a)$ and $(p_2,a)$ respectively, then $\frac{X_1}{X_2}$ will follow a Beta prime distribution of parameters $(p_1,p_2)$.
...

Is it possible to derive the joint probability mass function of two discrete random variables (categorical in my specific case) IF we know that they are perfectly correlated?
Let's assume for ...

I am a stats rookie and have a relatively basic question regarding the normal distribution of data.
If I measure a continuous variable under several different conditions/treatments, I look at the ...

Suppose $X_1,X_2,\dots,X_n$ are p-dimensional random variables with distribution $N_p(\mu,\Sigma)$. Let $X_{n\times p}$ is the data matrix. $\mathbb{Z}_{n\times p}= (n-1)^{-1/2}\left(I_n - n^{-1}\...

Let's say we have a random variable $Y$ defined as the sum of $N$ Bernoulli variables $X_i$, each with a different, success probability $p_i$ and a different (fixed) weight $w_i$. The weights are ...

I am doing bayesian analysis. Exploratory analysis shows the parameter might has a left skewed shape. So what kind of distribution should I used as prior distribution for this parameter? Any kind of ...

I have a rather funny situation here. There is this random complex number, $z$, with an unknown distribution $\rho_\lambda(z)$ which depends on a parameter, $\lambda$.
I can compute the moments and ...

Let, I have the following Frequency Distribution:
Which one would be the correct Grouped frequency Table if class-width = $1.0$?
$Table\#1$
$Table\#2$
Explain "Why".
What would be the answer if $\...

If we observe two censored distributions, where all observations above a cutoff are set at the value of the cutoff, how can we test whether the observable distributions suggest that the two censored ...

Suppose we have a known discrete probability distribution $X$ over $\{0,1\}^k$.
Given a sequence of binary values $e = (e_1, ..., e_n)\text{, where } e_i\in \{0,1\}^k$, what is the probability (or the ...

I have an empirical distribution that looks like the the image below and I hoping to model it with some parametric distribution. The X axis measures "number of ...

I need to compare a few distributions. I believe they all are non-normal with fat tails. How can I be sure of it?
I plotted the quantile plot for all of them, and I can see that they all have a fat ...

Suppose that I visualized a distirbution and noticed that it was multimodal. For example, I collected the heights of a bunch of students.
I notice that the distirbution is multimodal. How would I ...

The title says it.
If one wishes to analyze ternary outcomesâ€”that is categorical outcomes with specifically three values (-1,0,1)â€”are $\chi^{2}$ / contingency table tests and multinomial-logistic ...

I'm experimenting with replacement for normal distribution for my models.
So far, I tried Gamma and Inverse Gamma distributions. Gamma significantly underestimates the probability of the extreme ...

I am currently working with a dataset in which I have provided a numerical value (0 to 3) to different regions on a subject. The values correspond to the severity of the region affected (0 - not ...

Problem Description
I have simulated the movement of cars in a lane. The simulation model was first calibrated based on an observed car traffic. Now, I have vectors of speeds (collected every 0.1 ...

I have $ B $ bins and $ G $ balls, and each of the balls has a weight. I toss the balls uniformly into the bins. I select the $ K $ bins that have the highest weights as determined by the weights of ...

ESPN has partnered with IBM to use Watson to predict NFL player performance. I took at the underlying data and it includes a score distribution, which Watson indicates is a Fisk distribution.
The ...

I'm just currently getting into the world of Bayesian machine learning, with a lot of frequentest stats background, and I frequently find myself limited in my modeling by my lack of knowledge about ...

This is an obfuscated version of a real problem:
Each day I speak with some number of (distinct) girls.
I compute the Jaccard similarity index between two consecutive days:
$$
J(t)=J(t,t-1)=\...

Analyzing an an enterprise environment where large number of Windows end user devices have low disk space. To identify causes of the low disk spaces I ran scripts which provides the total size for ...

Let $f(x;\theta)$ be probability density function. Suppose that this pdf contains a proportionality constant $c$, so that $f(x;\theta) = c\cdot g(x;\theta)$, where $g$ is an integrable function. Is ...

Generally, I normalize variables using standard normal variates or (x-xmin)/(xmax-xmin)But this only works well for variables that are not truncated, for example ...

I apologize if I do not know the proper terminology, I will do my best to describe the problem. I have a computer model that gives me a set of 1000 possible outcomes for a single event. Currently, I ...

Quoting:
As can be seen in Table 1, the experimental and control group distribution were sufficiently normal for the purpose of conducting a $t$-test (skewness $<|2.0|$ , kurtosis $<|9.0|...

I am very new to this subject, but i've tried searching other questions and haven't found what i need.
I'm working on an application that will be promoted in physical meetings. Lets say, for example, ...

- probability
- normal-distribution
- r
- self-study
- mathematical-statistics
- random-variable
- hypothesis-testing
- bayesian
- sampling
- poisson-distribution
- chi-squared
- estimation
- binomial
- regression
- statistical-significance
- machine-learning
- uniform
- gamma-distribution
- conditional-probability
- fitting
- variance
- lognormal
- mean
- expected-value

- Employer makes me use what I believe to be an insecure website for HR functions. What to do?
- Continuous power between multi-gang boxes with 3 way switches
- Python Blackjack game
- Tikz and Secant Line diagram
- Why do bikes hardly ever skid while braking with the front wheel?
- Limit of matrix A raised to power of n, as n approaches infinity.
- Why is there no permutation in Regexes? (Even if regular languages seem to be able to do this)
- Bash sort array according to length of elements?
- Could people of the 14th century create an inline engine for use in aircraft and vehicles?
- Are there any indications why Roddenberry chose to make Star Trek a "battleship universe"?
- If someone wanted to pretend to be Satoshi by posting a fake signature to defraud people how could they?
- Science fiction series where in each novel, a man travels from planet to planet and helps the inhabitants in overthrowing their oppressors
- How to draw the following matrix in latex?
- I have 100 boxes. C of them have a gift. I can open up to 16 boxes. What is the number of C that will give me probability over 0.5 to find a gift?
- Giving a test lecture, what should I keep in mind?
- Is this quadrilateral cyclic?
- BASH: how to view command history in while loop?
- Does one call "regular" men "Sir" in the UK?
- Building circuit to amplify small sensor signals using an Instrumentation Amplifier and 24-Bit ADC
- Own implementation of Lazy<T> object
- Why Did God Directly Command Abraham to Sacrifice Isaac but Sent Angels to Stop Him?
- What happened to Nicholas Flamel's wife in The Crimes of Grindelwald?
- Algebra 2 textbooks that incorrectly claim that all solutions of polynomial equations can be found
- What makes the bicycles in Amsterdam suitable for riding with jeans on?