Get Ahead in Geometric Probability: Expert Guidance and Real-World Applications

Recent questions in Geometric Probability
Troy Kaufman 2023-03-11

What is the Common Ratio in GP?

Theresa Daugherty 2022-12-06

The degree measure of a semi-circle is1) ${0}^{\circ }$2) ${90}^{\circ }$3) ${360}^{\circ }$4) ${180}^{\circ }$

Sophie Marks 2022-11-21

Geometric Probability Problem, Random Numbers $0-1+$ Triangles.Randy presses RANDOM on his calculator twice to obtain two random numbers between 0 and 1. Let p be the probability that these two numbers and 1 form the sides of an obtuse triangle. Find p.

Ty Moore 2022-11-17

Negative Binomial Vs GeometricSo I am trying to get the difference between these two distributions. I think I understand them but the negative binomial has me a bit confused.The Geometric is the probability of some amount of successes before the first failure.The Negative binomial is the portability of some amount of successes before a specified number of failures? for example the number of successes before the 8th failure?

Kale Sampson 2022-11-17

Investigating the generalised Hamming distance of some code and information transmission of a binary code.Letting A be an alphabet of size a and $S={A}^{n}$. Meaning the set of all worlds of length n with bits chosen from the alphabet A. We now take $w\in S$.Assume $n=14$. How many words in S are of Hamming distance less than or equal to 4 from w?Secondly, assume $n=14$ and $a=2$ and that $w\in S$ is transmitted through a Binary Symmetric Channel with probability p of correct transmission for each individual bit. How would you generalise a formula for the probability that 5 or fewer errors will occur during transmission of w?

spasiocuo43 2022-11-15

approximate probability of geometric distribution using CLTFor $i\ge 1$, let ${X}_{i}\sim {G}_{1}/2$ be distributed Geometrically with parameter 1/2. Define ${Y}_{n}=\frac{1}{\sqrt{n}}\sum _{i=1}^{n}\left({X}_{i}-2\right)$Approximate $P\left(-1\le {Y}_{n}\le 2\right)$ with large enough n. Hint, note that ${Y}_{n}$ is not "properly" normalized.

Nola Aguilar 2022-11-15

Negative binomial distribution vs geometric distributiionHow can this question be geometric and also negative binomial. In order to join a group Peter needs 9 invitations.The probability that he receives an invitation on any day is 0.8, independent of other days.He joins as soon as he receives his 9 th invitation. Given that he joined on the 14 th day, find the probability that he receives his first invite on the first day.

piopiopioirp 2022-11-14

What is the probability that the quadratic equation $a{x}^{2}+x+1=0$ has two real roots?A number a is chosen at random within the interval (-1,1). What is the probability that the quadratic equation $a{x}^{2}+x+1=0$ has two real roots?For it to have its real roots, we must guarantee that $1-4a\ge 0$, or $a\le \frac{1}{4}$.

Uroskopieulm 2022-11-14

Derivation of a conditional probability mass function which involves Geometric and Gamma random variablesLet N be a geometric random variable with parameter p. Suppose that the conditional distribution of X given that $N=n$ is the gamma distribution with parameters n and $\lambda .$ Find the conditional probability mass function of N given that $X=x.$.

Ty Moore 2022-11-13

Geometric Distribution - ProbabilityHow we can proof that if $X\sim Geo\left(p\right)$Than: $Pr\left(X>a\right)=\left(1-p{\right)}^{a}$How can we proof it formally? There is an example for that to understand it intuitively?

akuzativo617 2022-11-11

On a certain discrepancy measure between probability distributions on the symmetric group of permutation ${\mathfrak{S}}_{n}$Let ${\mathfrak{S}}_{n}$ be the symmetric group of permutations on n objects and let P and Q be a probability distributions on ${\mathfrak{S}}_{n}$ (i.e P and Q are points on the n!-simplex). For $1\le i, let ${p}_{ij}$ be the probability that a random permutation $\sigma$ drawn from P ranks j ahead of i, i.e satisfies $\sigma \left(i\right)<\sigma \left(j\right)$. Consider the quantity $\mathrm{\Delta }\left(P,Q\right):=\sum _{1\le i.Is it possible to reasonably upper-bound $\mathrm{\Delta }\left(P,Q\right)$ in terms of some distance (e.g total variation) between P and Q ?

nyle2k8431 2022-11-10

Let E be the event of an even number of successes.${u}_{n}$: Probability of E occurring at the nth trial not necessarily for the first time${f}_{n}$: Probability of E occurring at the nth trial for the first timeLet U(x) and F(x) be the corresponding probability generating functions and from that we have the equation$U\left(x\right)=1/\left(1-F\left(x\right)\right)$

undergoe8m 2022-11-09

How come if X is a Geometric random variable, then $P\left(X>x\right)={q}^{x}?$

inurbandojoa 2022-11-08

An upper bound on the expected value of the square of random variable dominated by a geometric random variableLet X and Y be two random variables such that:1. $0\le X\le Y$2. Y is a geometric random variable with the success probability p (the expected value of Y is 1/p).I would be grateful for any help of how one could upperbound $\mathbb{E}\left({X}^{2}\right)$ in terms of p.

inurbandojoa 2022-11-08

Probability that at least 4 out of 365 times I try, I need more than 5 flips before getting a tailsSuppose I flip a coin until I get a tails. Let X be the number of flips this takes. What is the probability that there are at least 4 days in a year where I needed more than 5 flips to get a tails?Is this kind of question combining geometric and exponential distributions with some kind of conditional probability? I'm unsure how to compute this.

Emmanuel Giles 2022-11-08

An identity involving geometric distributionLet $\left(\mathrm{\Omega },\mathfrak{A},P\right)$ be probability space and $X:\mathrm{\Omega }\to {\mathbb{N}}_{\mathbb{0}}$ be a geometrically distributed random variable with parameter $p\in \left(0,1\right)$ $X\backsim \text{Geo}\left(p\right)$. Show that

Ty Moore 2022-11-07