Tagged Questions

Questions on using, finding, or otherwise relating to probability distributions, pdfs, cdfs, or the like.

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Box Muller Transform - Proving that Z is Normal Distribution

I'm studying the Box Muller transform and I cannot see how Z0 and Z1 represent standard normal distributions. I've looked at the wikipedia page for the box-muller function but they don't seem to have ...
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Challenging Joint Probability Question

This is quite a challenging question I've been having trouble with lately and seems to be an atypical example of a joint distribution question - While I can derive the marginal density of $X$ simply ...
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Prevalence estimates based on randomized sample of clinical data

This is probably one of the more straight forward questions on here but here it is: I want to use a random number generator to sample X number of charts to look for the # occurrences of Y event. So ...
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CDF, PDF, and integral with respect to a function

In a certain textbook, I see the Cumulative Distribution Function (CDF) of a continuous random variable X defined as $$\int_{-\infty}^{x'} dp(x)$$ where p(x) is the Probability Density Function of X. ...
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An Airplane Probability to reach Oklahoma??

An airplane is built to be able to fly on one engine. If the plane' s two engines operate independently, and each has a $1\%$ chance of failing in any given four-hour flight, what is the chance the ...
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Moment-generating functions problem, total time before success at performing a task?

I'm facing moment-generating functions for the first time so I'm trying to get some practice and I'm stuck... Someone's trying to succeed at performing a given task. At each trial he either stops ...
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Challenging Marginal Probability Question

I've been stuck on this question for some time now - While I can derive the marginal density of X simply from the uniform distribution, I am at a loss for how the marginal density for Y and the joint ...
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generating a random probability mass function with uniform $p_i$'s

I would like to find the random probability mass function of a tuple $(p_1, p_2, ..., p_n)$ such that each variable is distributed such that $$p_i \sim U(0,1)$$ individually, but that every tuple ...
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Interesting Probability Question - Birthday Problem Variation

Suppose at a hipster eatery they make craft pickles. At this eatery they have $n$ pickle makers (picklers). Every day each pickler makes $10$ jars of pickles. Whenever any pickler has a birthday, ...
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The bug “probably” gets stuck!

Consider a regular tetrahedron with vertices $A,B,C,D$. A bug starts crawling from $A$. The bug moves from one vertex to the other along the edges continuously until it reaches $D$, where there is ...
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Expected Min/Max when picking numbers between 0 and 1

Suppose you pick two numbers between $0$ and $1$ with each number being picked at equal probability. What is the expected min/max of these two numbers? What if you picked ten numbers from $0$ to $1$? ...
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How many ordered quadruples (a,b,c,d) satisfy a+b+c+d=18, where a,b,c,d are odd positive integers? How many ordered quadruples (a,b,c,d) satisfy a+b+c+d=18, where a,b,c,d are integers such that |a|,|...
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Is the y axis on a PDF actually meaningless?

This idea popped in my head when I was reading this post on the normal distribution and the y-axis. My question is (and taking advantage of a nearby computer), a PDF inputs one value and returns ...
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Assume $1\leq\ k<m<n$ are positive integers and $X_1,X_2,...X_n$ are i.i.d. Geometric($p$) random variables. For all $j\geq\ k$ define $I_j=[(i_1,i_2,...,i_k):1\leq\ i_1<i_2<...<i_k\leq\... 0answers 70 views Sum of Lomax random variables Suppose$X_1,X_2,\cdots X_n$are$n$i.i.d Lomax random variables with pdf$f(x)=\frac{m}{(1+x)^{m+1}},x\geq 0,m\in \mathbb N$. I need to determine the pdf (or cdf) of the sum$S_n=\sum_{i=1}^{n}X_i$. ... 0answers 43 views For fun, how many paths are there in a flow matrix? I just got done doing the whole flow-matrix percolation exercise in programming. That is a situation where you have, for simplicity, an$n\times n$grid of 0s and 1s. 0s represent blocked sites and ... 1answer 236 views Probability from multiple trials This questions is from a practice mid-term that I don't have a solution to. A monkey in a research lab is given 6 tiles with the letters AAABNN. On each trial the monkey randomly arranges the ... 0answers 37 views Why the doubly non-central F distribution does not have a mean or variance if the denominator degree of freedom is less than or equal 2 ?? Normally the doubly non-central F distribution is generated by the division of two non-central chi squared Random Variables,, so what is the the problem of using any famous formula to get the mean of ... 1answer 25 views What is the probability of success? If I have 12 Possible questions, of which 5 are asked and I only need to answer 2 of them, what is the probability of my success (i.e., I am able to answer 2 of the 5 asked questions) if I learn 2 of ... 3answers 60 views Symmetric Distribution of Random Variable Prove: Let$X$and$Y$be random variables with the same distribution. If$X$and$Y$take only two values​​, then$X - Y$are symmetrically distributed around zero. Note: 1 - You can use ... 2answers 74 views Conditional Probability - chance for an event to happen I am learning probabilities at the moment and I have come across this problem: A person takes four tests in succession. The probability of his passing the first test is p, that of his passing each ... 2answers 48 views Probability CDF question on highest number of marbles pulled out I'm kinda stuck on this problem. Here goes: An urn contains n marbles, numbered 1, 2, . . . , n. Suppose k < n marbles are drawn from it at random without replacement. Let X denote the highest ... 2answers 404 views A random variable$X$uniformly distributed over the interval$[0, 2\pi]$A random variable$X$distributed over the interval$[0, 2\pi]$a) the pdf of$X$b) the cdf of$X$c)$P(\frac{\pi}{6} \leq X \leq \frac{\pi}{2})$d)$P(-\frac{\pi}{6} \leq X \leq \frac{\pi}{2})$... 3answers 94 views Find the pdf of T = X + Y Let (X,Y) be a random point chosen uniformly on region R = {(x,y) : |x| + |y| <= 1}. I need to find the pdf of T = X + Y. I know the joint density is just equal to 1/(area) = fxy(x,y) = 1/2 for |x|... 0answers 83 views Probability Distribution for a Weird Card Game I promise this is not for a homework problem, even though this sounds like only something a professor would dream up. Here is the game: I begin with a deck of 13 cards: 1 through 10, Jack, Queen, and ... 1answer 22 views How is this Variance found in this old question? On this question: Probability: Normal Distribution they find these values:$\hat\mu = .05(150) = 7.5\space,\hat\sigma = \sqrt{150(.05)(.95)} = 2.67$I see how they got$\mu$, but how did they get$\...
I am stuck on the following proof that I found in Dellacherie-Meyer's book "Probabilities and potential B", p. 119 (increasing processes and projectors). Given a map $a$ on $[0,\infty [$ which is ...