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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Doubtful answer for conditional probability question

There's a traffic light in a city which works properly, but sometimes it is faulty. If it functions properly today, there is a 95% chance that it will not malfunction tomorrow. However, if it is ...
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0answers
17 views

Expected number of rolls on a 200 sided die to roll a 1?

We have a 200 sided die and want to know how many rolls is expected to roll a 1. How would I go about calculating this?
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2answers
34 views

what is the meaning of probabilities P(A − B)?

Let $A$ and $B$ be two mutually exclusive events. What is the meaning of $P(A − B)$?
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1answer
21 views

Sum of two uniform independent random variables

I would like to find the cdf of $Z=X_1+X_2$, with $X_1\sim U(0,1) $, $X_2\sim U(0,2)$ I always prefer to find the cdf instead of the pdf with convolution, and this time I am having troubles with the ...
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0answers
18 views

Permutations & Combinations

How many 7-digit number's with no repeated digits contain a 3 but not a 6? The number does not start with zero. $$7 \cdot P(8,6) = 7 \cdot 20160 = 141120$$ because 3 can be in 7 position, and then 6 ...
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1answer
14 views

Approximating a joint pdf using normal density of two independent variables

I know that given these two random variables (which correspond to the $x$ and $y$ coordinates of a random walk after $n$ steps, their joint probability density function can be $approximated$ by a ...
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1answer
40 views

If $X_n\rightarrow X$ in mean square, then $\mathbb{E}(X_n)\rightarrow \mathbb{E}(X)$ [on hold]

How do I show that if $X_n\rightarrow X$ in mean square then $\mathbb{E}(X_n)\rightarrow \mathbb{E}(X)$ using the Cauchy-Schwarz inequality?
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3answers
14 views

Algebraic simplification of likelihood ratio

Can someone help me understand how this: ...
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1answer
14 views

Probability Question using Poisson distribution

On average, an employee receive 25 emails each day, of which 60% are ‘spam’. What is the probability that the employee will receive exactly 15 ‘spam’ emails tomorrow? My methodology is such: $$ ...
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0answers
23 views

Calculate P(X=Y)

I have a question that asks me to calculate $P(X=Y)$. The probability is based on $4$ trials of a binomial experiment. I was given the $pmf$ of $X$ in the following table: $$\begin{array}{c|c|c|c|} ...
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1answer
24 views

Probability of choosing a combination [on hold]

A person has $8$ red pills and $8$ blue pills. He chooses $8$ pills at random. What is the probability that the chosen pills are $4$ red and $4$ blue?
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0answers
24 views

Simple Probability of Playing Cards

An ordinary deck of playing cards has four suits: hearts, spades, diamonds, and clubs. Suppose you have a reduced deck of eight playing cards, consisting of four aces and four kings. I draw two cards ...
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1answer
20 views

Probability Another Playing Card question — twist

I completely understand the questions of probability of drawing 2 cards without replacement -- getting a heart or a face card. I add the probability of getting a heart with probability of getting a ...
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1answer
20 views

Is this chain irreducible and/or Aperiodic? What is its equilibrium mass function?

Consider a Markov chain with outcomes $\{0,…,n\}$ and transition probabilities $P_{i,i+1}=p$ $P_{i,i−1}=q$ for $1\le i\le n−1$ and $p+q=1$. Assume also that $P_{0,1} = P_{n,n−1} = 1$. Is this chain ...
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1answer
23 views

probability, random walk, Markov chain question

Let $P$ be a transition matrix for a regular Markov chain and let $w$ be it’s equilibrium vector. Show that $w$ has no zero entries.
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3answers
67 views

finding the probability to get a diploma

For getting a diploma a person needs to go to $3$ interviews at $3$ teachers: $A,B,C$. In each interview a teacher can give a positive opinion or negative opinion. The person will go to interview at ...
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1answer
13 views

Probability function and distribution - taking out fish from a pool

In a pool of fish there are 4 fish of type A, 3 fish of type B, 2 fish of type C, 1 fish of type D. We take out fish without returning them until we get fish of type C for the first time. ...
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1answer
56 views

Average distance between 2 points on surface of sphere?

How can I find an average distance between two points lying on surface of a sphere of a certain radius? More importantly : can knowing the average distance between two points on surface of a disk ( ...
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1answer
12 views

Odds of drawing multiple rounds of rock paper scissors.

OK, so the back story for this is me and my friend often decide things on a quick game of rock paper scissors. I think on this occasion it was for who would get up and answer the door when the pizza ...
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1answer
16 views

Binomial distribution tail inequality

Let $X \sim \mathrm{Bin}(n,p)$ does there exist $l$ ideally $l=f(n)$ such that $P(X<l)=o(1)$ in the limit $n\rightarrow \infty$? I'd be looking for the largest possible $l$.
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1answer
13 views

Application $\pi$-$\lambda$ lemma one-sided Markov shift

Let $(S_k^{\mathbb{N}},\Sigma_k^{\mathbb{N}},m,\tau)$ be the probability preserving transformation of the one-sided Markov shift, where $\Sigma_k^{\mathbb{N}}$ is the $\sigma$-algebra generated by the ...
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0answers
25 views

At a step, we either increment or decrement $t$. If $|t| = x$, the program halts. What is the chance of the program still running after $n$ steps? [on hold]

We start with $t = 0$. At each step, we either increment $t$ with probability $p$ or decrement $t$ with probability $1-p$. If $|t| = x$, the program halts. What is the chance of the program still ...
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1answer
30 views

Poisson Distribution to Calculate plane crashes

The number of passenger planes that crash every day follows the Poisson distribution with parameter p. The number of crashes each day is independent. What is the probability of exactly 3 planes ...
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0answers
31 views

Conditional expectation over a convex set

Let $\boldsymbol{X}$ be an $\mathbb{R}^d$-valued absolutely continuous and integrable random vector. Further, let the cdf $F$ of $\boldsymbol{X}$ be strictly increasing in each component on ...
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2answers
42 views

Mean age among employees in a company.

In a company there are 32 men and 59 women. Male mean age is 48.5 and female 39.2. One of the women (47 years old) ended working at the company and was replaced with a 23 year old man. Calculate the ...
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0answers
25 views

Probability to draw all items (Simplification)

I was calculating the probability to draw all items in a list of N items, by picking one randomly, replacing it in the list, etc. I found this formula after n picking. $$ \sum_{i=0}^N ...
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1answer
27 views

Average distance between two random points in a square

A square with side $a$ is given. What is the average distance between two uniformly-distributed random points inside the square? For more general rectangle case, see here. The proof found there is ...
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1answer
20 views

Confusion about probability question

Some friends are sitting together playing a game that involves rolling dice. On one turn, a player rolls six 6-sided dice and gets one of each number showing. Another player sees this and asks "what ...
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1answer
15 views

How to get the value of 'scaled' binomial distribution?

People kindly told me that there is not a equivalent popular distribution for $aX$ when $X$ is distributed as Binomial, but it is just a 'scaled' distribution. Here, $a$ is a positive constant. ...
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1answer
18 views

Poisson Probability (Shopkeeper Sales)

SOLUTIONS: (A) 0.1804 (B) 0.0166 (C) 0.3233 Mean = 2/7*5 (a) x = 3 (b) x > 5 I'm still unsure how to approach each question, because I still get the wrong answers.
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1answer
29 views

pdf: What is the distribution of aX when X ~ Binomial / Gaussian

Question When $X$ is distributed as binomial or Gaussian, is $aX$ equivalent to some famous distribution? Here, $a$ is a real and positive number. Background I know a general formula giving $aX$'s ...
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1answer
27 views

Joint Probability with many values

Consider I have the following tree structure which provides the relation between various entities. Associated with this, I have the following table with data. ...
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0answers
35 views

Convert min to max probability

Assuming $Y=min(w_1,\ldots,w_n)$ , $w_i\sim N(\mu,\sigma^2) i.i.d$ I want to express $Y$ in terms of the $Q$ function. Knowing that $Y=min(w_1,\ldots,w_n)=-max(-w_1,\ldots,-w_n)$ $P(Y\leq y)= ...
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0answers
12 views

Comparing results of calculated probability and practical probability [on hold]

I am planning to compare probability that comes from theory and practical experiment. So here the detail of my experiment: I have black box B where there are N lines as input and N lines as output, I ...
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1answer
16 views

Poisson Distribution Worded Problem (Typist & Corrections Question)

The rate is 1/800 The mean is 1/800*(200) (a) 1 - poissCdf(1/800*200,0,1) = 0.026499 0.026499 = Probability that a page is deemed unsatisfactory OR Probability that a page needs to be retyped ...
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0answers
14 views

Most efficient estimator

$X_1,...X_n$ is a random sample of size $n$ from a population with mean $\mu$ and variance $\sigma^2$.There are three estimators for $\mu$:  $\hat\mu _1=\frac{x_1+x_2}{2}$ $\hat\mu ...
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1answer
27 views

Is there any simple formula for this probability distribution of random walk?

Assume $\{S_n\}_{n\geq 0}$ transits as follows: $S_0=0$, for $k\geq 1$, $P(S_{n+1}=k+1|S_n=k)=\alpha$, $P(S_{n+1}=k|S_n=k)=\beta$ and $P(S_{n+1}=k-1|S_n=k)=1-\alpha-\beta$, where ...
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0answers
25 views

Game of Keno from Sheldon Ross Chapter 4

I am facing with the following problem: A game popular in Nevada gambling casinos is Keno, which is played as follows: Twenty numbers are selected at random by the casino from the set of numbers 1 ...
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1answer
19 views

Expected value of Bernoulli with probability of success Gaussian distributed

I have a circle with centre $(0,0)$. I am generating Matlab code to include $N$ neurons in a neural network. The probability of including individual neurons in a network decays exponentially with ...
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0answers
33 views

Calculating the probability of being caught

This is a game theory problem I am working on. I apologize if this question is elementary; my probability is pretty rusty and I'm also new to this - I just started working on my PhD and after being a ...
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0answers
33 views

Random Walk Question - what is the probability of eventually reaching the origin? [duplicate]

Consider the random walk $S_n$ given by $S_{n+1} = S_{n} + 2$ with probability $p$ ; $S_{n+1} = S_{n} - 1$ with probability $1-p$. Assume that $S_0 = n > 0$ with certainty. What is the ...
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0answers
34 views

Show the equilibrium vector of a transition matrix for a Markov Chain has no zero entries

Let P be a transition matrix for a regular Markov chain and let w be its equilibrium vector. Show that w has no zero entries. I am thinking using the fundamental limit theorem for regular chains for ...
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1answer
34 views

What distribution it is based on the histogram? [on hold]

I generated this histogram in r and was trying to determine which distribution I should use, my guess is normal or Binormial. But I'm not sure, can anyone help please?
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1answer
21 views

Setting up the expected value for $x_t=\sin(2\pi U t)$.

We have the series $x_t=\sin(2\pi U t)$ where $t=1,2,3,\ldots$ and $U$ is uniform on the interval $(0,1)$. I have to find the expected value of $x_t$. I always thought that if $X$ is a continuous ...
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1answer
13 views

Joint Density Functions

Let X have density f(x)=2x for 0 a) Give the joint density function of (X,Y). Calculate the probability P(Y-X>1.5) Since X and Y are independent, can I just say that f(x,y) is just equal to 2x? And ...
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1answer
59 views

Is conditional probability $P(A\mid B)$ proportional to $P(B\mid A)$?

It feels a bit odd but since $$P(A\mid B) = \frac{P(A,B)}{\sum_A P(A,B)} \propto P(A,B)\text{ and }P(B\mid A) = \frac{P(A,B)}{\sum_B P(A,B)} \propto P(A,B)$$ can we say that $P(A\mid B) \propto ...
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1answer
15 views

A question about iid observatins $(X_1, \cdots ,X)n)$, knowing that $f_X(x) = ve^-vx$ , with x>0 and v>0.

How do I show that X also have gamma distribution with parameters $nv$ and $n$? I know about the relationship between exp and gamma distributions, but i don't know how to solve this.
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0answers
21 views

Multiple Anihilating Random Walks in a Ring (cycle)

I've been trying to solve this problem for a long time. Problem Let $R$ be a cycle with $2n$ nodes and assume there are $2k$ particles performing a simple random walk in this ring (i.e., they have ...
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0answers
9 views

Calculating variance & expected value of a statistic with exponents

I am trying to calculate of a statistic: $Var(\frac{1}{1 + 1/n \sum_i x_i})$. Thus far, I have $=E[(1 + 1/n \sum_i x_i)^{-2}] - E[(1 + 1/n \sum_i x_i)^{-1}]^2$. How do you deal with exponents inside ...
9
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3answers
1k views

Curious about a made-up paradox

I have thought up a paradox, that may already exist, but I do not know what it's called. It's bothering me though, so any help regarding solving it or proving it impossible would be appreciated. In ...