This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

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1answer
25 views

poisson distribution finding possibility(revised)

It is known that for a laboratory computing system the number of system failures during a month has a Poisson distribution with a mean of 0.8. The system has just failed. Find the probability that at ...
0
votes
1answer
26 views

Bernoulli trial - formula derivation

I wanted to see I understand Bernoulli trial correctly. It's not a single experiment. Instead, we treat it as a set of $n$ consecutive experiments - each can end with success (with probability $p$) or ...
2
votes
4answers
107 views

Dice roll probability, at least 9 total?

If I have two dice with $6$ sides each, what is the probability of me rolling atleast $9$ total? I think I'm correct when thinking that the probability of rolling a $9$ is $\frac{4}{36}$, that is ...
2
votes
1answer
49 views

Show that a Markov Chain is ergodic

Let $Y_n$ be iid random variables with values 1,2,3..n so that $P[Y_i=j]=p_j>0$, where $i\leq1$ and $1\leq j\leq n$. I think I managed to show that $Y_n$ is a Markov chain using the definition, ...
1
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1answer
35 views

Stronger version of Markov Chain

I have just started looking into the concept of Markov chains and I was wondering if anyone could help me with this problem. Let $X_1, X_2, ...$ be a Markov chain with the state space $S$. I need ...
3
votes
2answers
63 views

Chess Probability 8 rooks

You have 8 rooks. What is the probability of placing all 8 rooks on an 8 by 8 chess board with out one being able to hit each other? But there's a catch of course..one of the spaces is unavailable to ...
-2
votes
0answers
23 views

Bayes Probability computation [on hold]

I received a HW in which i have some problems. I will be very grateful if anyone could help me out. This is the question: Consider a line segment whose length equals 1. We throw a first ball that ...
-1
votes
1answer
31 views

Process adapted to Filtration [on hold]

Here is the definition I have been given : A process $(X_t)$ is adapted to a filtration $(\mathcal F_t)$ if $X_t$ is $F_t$ measurable, for all t > 0 , i.e : $X_t^-1 (\mathcal B)$ belong to ...
0
votes
1answer
29 views

How do I compute $P(X=Y)$? for independent random variables with with geometric distribution.

let $X$ and $Y$ be independent random variables with geometric distribution and parameter $p\in(0,1)$ How do I compute $P(X=Y)$? Any help would be greatly appreciated.
2
votes
1answer
51 views

Birthday Problem [on hold]

What is the approximate probability (in percentage) that at least $2$ people in a group of $6$ randomly-selected have a birthday on the same day of the week?
0
votes
1answer
44 views

Kruskal Wallis - Effect size

I analyse 4 algorithms and 3 sets of metrics for each algorithm in which I apply the non-parametric Kruskal-Wallis test for each metric to detect any differences in performance between these ...
0
votes
1answer
105 views

Probability of no more than three heads given that at least one toss resulted in heads

You toss a coin four times. Find the probability of no more than three heads given that at least one toss resulted in heads. So if I set event A as no more than three heads and B as at least one ...
1
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2answers
24 views

Show $\lim\limits_{m\to\infty}P(n\leq m)=1$ for some function $n:\Omega\to\mathbb{N}$

Suppose that $(\Omega,\mathcal{F},P)$ is a probability triplet and $n:\Omega\to\mathbb{N}$ is some measurable function (in particular, $n(\omega)$ is finite for each $\omega\in\Omega$). I'm ...
-1
votes
0answers
25 views

Expected value problem

Imagine the following scenario: Several players contribute coins to a pot in a random order and without knowing what other players have contributed. When every player has added his stake, the coins ...
0
votes
1answer
27 views

In Bayes' theorem, what is little $p$?

In Wikipedia's conjugate prior article, Bayes theorem is given as: $$p(\theta|x) = \frac{p(x|\theta) \, p(\theta)} {\int p(x|\theta') \, p(\theta') \, d\theta'}.$$ What is $p$ here? Is it the ...
1
vote
1answer
46 views

Conditioning events on a conditional expectation

Let $X_0=a$ for some $0<a<1$ and for $n \geq 0$, let $\mathbb{P}(X_{n+1}=X_n/2|\mathcal{F}_n)=1-X_n$ and $\mathbb{P}(X_{n+1}=(1+X_n)/2| \mathcal{F}_n)=X_n$. Show that X is a martingale. This ...
-2
votes
1answer
15 views

About random variable X, which is a certain number of cars that can pass over a bridge in a 5 minute period [on hold]

Random variable X, which is number of cars that can cross a bridge in a 5 minute period. Probability that at most, 2 cars will cross the bridge in 5 minutes Number of Cars Frequency 0 ...
2
votes
1answer
25 views

Difference between Frequentist and Bayesian approach to Statistics

What is the difference between the Frequentist vs. the Bayesian approach to Statistics? Would someone be so kind to come up with a simple example that shows how the approaches and possibly the ...
1
vote
0answers
18 views

Maximum likelihood estimation when the density is F(x/θ)=1-(1-x)^θ

I am Working to find the maximum likelihood estimation (MLE). The commulative distribution function is given as F(x/θ)=1-(1-x)^θ So first i find the Pdf by derivatiting the above function which is ...
0
votes
0answers
28 views

Dice expirements and random variable?

Suppose I define a random variable $X$ such that it represents the sum on the dice thrown. Now there are two ways to do the experiment I use 2 dice, note their individual $X_i$ (R.V) and then find ...
-4
votes
2answers
70 views

How to find the probability mass function (PMF) of X and Expectation of X [on hold]

Suppose that you have n switches (n > 1), and that the probability of any individual switch not working is p. You consider two strategies for testing the n switches: • Strategy A: Test each switch ...
-4
votes
0answers
29 views

probability theory regarding death [on hold]

The probability that a man who is 85 year old will die before attending the age of 90 year is 1/3. x, y, z and w are four persons who are 85 years old. What is the probability that x will die before ...
-1
votes
0answers
14 views

Looking for a formula to evaluate likelihood of a successful event with increasing occurrences

Perhaps I am over thinking this problem, but I could use some help. Constant: Chance to receive a broken bone is 15% Variable: Number of attackers Example: Assume that John Doe gets in a fight with ...
0
votes
2answers
22 views

Density of conditional distribution

Let $X$ be a continuous random variable with density function $f(\cdot)$. Define $Y = 2X$, another continuous random variable. I would like to determine the conditional density of $f_{Y|X}(y|x)$. It ...
0
votes
1answer
18 views

Supposedly easy hypergeometric probability question? Are my answers right to parts i and ii and how to do iii?

Fix positive integers $r_{1} \leq K_1$ and $r_{2} \leq K2$ and let $N=K_1+K_2$ and $n=r_1+r_2$. A subset $S \subseteq \{1,2, \ldots, N\}$ having $n$ elements is chosen. i) How many possibilities are ...
1
vote
0answers
30 views

Sample space for sampling from (a large) student population…?

10% students left handed. 30% blue eyed. 5% both left handed and blue eyed. Two students are chosen at random and whether or not each was blue eyed or left handed is noted. Assuming population of ...
1
vote
0answers
25 views

Simulating r.v.'s from a joint density by rejection sampling in R. Continued

I wish to sample variables $v$ and $w$ from the joint density $$(v+w)e^{-\frac{(v+w)^{2}}{2x_{0}}-2\mu v-(\mu -\lambda )w},$$ where $x_0$, $\mu$ and $\lambda$ can be seen as positive constant. Since ...
0
votes
0answers
27 views

Applying chain rule in probability?

Let $X,Y$ be random variables with distribution functions $F_X(x)$, $F_Y(y)$. Let $W(u,v)=max\{0,u+v-1\}$. why can we take the following limits "inside" $W$? $lim_{(x,y)\to ...
0
votes
2answers
25 views

Probability of intersection greater than product of probabilities?

Is it true in general that $P(A\cap B) > P(A) P(B)$? If yes, why?
0
votes
2answers
32 views

Probability of tossing five coins and getting at least one head

here is my dilemma. I want to know the probability of getting at least one head in five coins being tossed one after the other. Could you help me get the logic of this as it involves both mutually ...
-1
votes
1answer
21 views

Probability of forming a committee of seven with 5 men [on hold]

Seven people are randomly selected from a group of 10 men and 11 women to form a committee. Find the probability that exactly 5 men are on the committee.
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0answers
10 views

$E[R^2]$ by saprcings

If you define R as the range: R=X_(n)-X_(1) and let be the sparcings S_r=X_(r+1)-X_(r), I found in this article http://www.ime.unicamp.br/sinape/sites/default/files/article.pdf page 7, than ...
0
votes
0answers
31 views

Probability of succesful rolls of different sided dies

This seems so simple, but I'm not sure how to calculate it. I have one six-sided die and one 12-sided die. What is the probability that, on a roll of both dice, that the six-sided die will win? ...
1
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0answers
25 views

Prove that the variance of a discrete random variable increases with a parameter

I have an infinite number of known probability density functions $f_1(x),f_2(x),f_3(x),...$. The PDFs $f_k(x)=\sum_{j=1}^k v(A+j-1)e^{-v(A+j-1)x}\binom{k}{j-1}q^{j-1}(1-q)^{k-j-1}$. Let ...
0
votes
1answer
24 views

Inequality involving probabilities

While working on stochastics processes, I have found the following inequality, which I have not been able to proof: Let $h>l>1$ and $0\leqslant p\leqslant 1$ (probability). Then ...
0
votes
1answer
94 views

least mean squares(conditional expectation) problem

The lifetime of a type-A bulb is exponentially distributed with parameter $2$. The lifetime of a type-B bulb is exponentially distributed with parameter $3$. You have a box full of lightbulbs of the ...
0
votes
1answer
18 views

PDF & values of a random variable

Let $X: \Omega \rightarrow \mathbb{R}$ be a random variable and $f_X(x)$ its probability density function. Is it true that $\{x : f_X(x) = 0\} \cap X(\Omega) = \emptyset$? For one, if $X \sim ...
1
vote
1answer
41 views

How to prove / disprove these conditional probability statements?

I was browsing a well known technology board and someone posted a pretty standard question about conditional probabilities. As this happens to be the current subject of my lectures (just starting), I ...
0
votes
0answers
15 views

probability question regarding coin flips [on hold]

if i flip a coin 10 times, what is the probability that i get 5 straight heads then 5 straight tails?
0
votes
0answers
19 views

Maximum likelihood estimation (MLE) calculation [on hold]

Find Maximum likelihood estimation (MLE) of theta. Find the MLE's probabiliy distribution. this is what i tried, but i dont know how to simplify it?
0
votes
1answer
38 views

Showing that all possible outcomes are equally likely.

Question: Consider a sequence of independent trials, with each trial being a success with probability $p$. Given that the $k$th success occurs on trial $n$,show that all possible outcomes of the ...
0
votes
1answer
38 views

Three containers first contain $r$ red balls second $g$ green balls and third contains $b$ blue balls

Three containers first contain $r$ red balls second $g$ green balls and third contains $b$ blue balls ..at all I want to draw 3 balls and it doesn't matter from which container .. the problem is to ...
-1
votes
0answers
20 views

Analytical challenge - solve how 100 people can all meet among each other! [on hold]

100 people in an audience are to divide into two groups, green and red. The red group are to be seated as follows - 5 people on each 10 round tables. The green people are to rotate as follows - 5 ...
0
votes
1answer
27 views

How to interpret combination and permutation problems?

This is more of a methods question than asking for a specific answer: In revisiting statistics and attempting various problems, I am curious if anyone has any insights on how to "see" the route to ...
0
votes
0answers
35 views

Probability density function for distance between two points.

Two points are chosen randomly inside a circle (and even on the circumference) with radius $r$ What is the probability density function of the distance between the points? I would be very grateful.
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votes
2answers
29 views

Checkerboard Expected Value Question

A checker is placed in a random square of an ordinary $8\times 8$ checkerboard (with all squares being equally likely). Then, checkers are placed in all squares that are below and to the right of the ...
0
votes
1answer
34 views

Variance of a Gaussian Random Variable

Show Variance of a Gaussian random variable $N(\mu,\sigma^2)$ and I know $\mathbb{E}(X)^2 = \mu^2$. So I need $\mathbb{E}(X^2)$ = $\int_{\mathbb{R}} x^2 \frac{1}{\sqrt{2\pi\sigma^2}} ...
0
votes
0answers
14 views

perfect coin is tossed n times. Let Sn denotes the number of heads obtained. What is the expectation of Sn?

The Problem is: A perfect coin is tossed n times. Let Sn denotes the number of heads obtained. What is the expectation of Sn? I got to E(Sn) = $\sum_{n=1}^{+\infty} \space\space\space Sn ...
0
votes
1answer
26 views

Determining the UMVUE for a discrete scaled uniform sample.

I would greatly appreciate some help. Below, I'll try to explain what I want to do and show my progress. To begin with, let $X_{1}, \dots, X_{n} \sim \mathrm{unif}\{1, 2, \dots, N\}$. Let $T = ...
-1
votes
2answers
98 views

How to find probability of random variables and expected value and variance [on hold]

Here is my homework that I am stuck on: Question $1$. ($9$ points) Suppose you have a playlist consisting of five songs that you play in “smart shuffle” mode. In this mode, after the current song is ...