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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-1
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0answers
6 views

Comparing results of calculated probability and practical probability

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 ...
0
votes
0answers
8 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 ...
0
votes
0answers
7 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 ...
0
votes
0answers
7 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 ...
0
votes
0answers
17 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 ...
1
vote
0answers
10 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 ...
1
vote
0answers
23 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 ...
2
votes
0answers
25 views

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

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 ...
-3
votes
0answers
17 views

Is this Markov Chain irreducible? Aperiodic? What is its equilibrium mass function? [on hold]

Consider a Markov chain with outcomes $\{0,\dotsc, n\}$ and transition probabilities \begin{align*} P_{i,i+1} &= p \\ P_{i,i-1} &= q \end{align*} for $1\leq i \leq n-1$ and $p+q=1$. Assume ...
-1
votes
0answers
11 views

Show the equilibrium vector of a transition matrix for a Markov Chain has no zero entries [on hold]

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.
1
vote
1answer
30 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?
1
vote
1answer
18 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 ...
1
vote
1answer
12 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 ...
1
vote
2answers
43 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 ...
0
votes
1answer
12 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.
1
vote
0answers
16 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 ...
0
votes
0answers
6 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 ...
7
votes
2answers
439 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 ...
0
votes
0answers
8 views

Calculating normalization constant in circle detection process

I'm doing some research in computer vision, and I need to calculate if two edge points correspond to the same circular object, but i have few questions. Formula is: where: pi and pj are two ...
0
votes
1answer
22 views

Definition of an absolutely continuous random variable

Just what is the proper definition of an absolutely continuous random variable? It's supposed to be something like: $$\mathbf{P} (A) = \int_A f d \mu$$ for some Borel set $A$. But what is $\mu$? Is ...
-4
votes
0answers
17 views

Naive Bayes' classifier [on hold]

Here's the problem set: I got the first two sections down but I have no idea how to do the third section. Can anyone help?
2
votes
2answers
28 views

Probability of a pair of red and a pair of white socks among five chosen [on hold]

In the box are seven white, five red and three black socks. Socks are considered to be a pair if they have the same color. Five arbitrary socks are selected at random from the box. Find the ...
0
votes
0answers
25 views

proof that some expected value equal to $\theta (\log n - \log k)$

So here is the problem - Given the following equation: $(c_2\cdot \log n) - (c_1\cdot \log k)\le E(X)\le 1+ (c_1\cdot \log n) - (c_2\cdot \log k)$ When $c_2,c_1\gt0$ and also $c_1\gt c_2$ In ...
-1
votes
1answer
27 views

Geometric Brownian Motion [on hold]

I am new there. How can I calculate following expected value: $$E[X(s)\times X(t)]$$ where $X$ is Geometric Brownian Motion, i.e. $X(t) = exp[(\mu - 0.5\cdot \sigma^2)t + \sigma\cdot W(t)]$ ...
-3
votes
0answers
23 views

Probability theory's problem [on hold]

We number a regular icosahedron's faces (it has 20 faces) and start to throwing up randomly, and note the number of the face which it has arrived. Writing down the numbers until the sequence of the ...
0
votes
2answers
32 views

Probability to get from point A to point B.

In the photo each dot is a city and each blue segment a road. Each road is blocked with probability 1/3 and free with probability 2/3 (independence among all roads). What is the probability that it is ...
0
votes
0answers
15 views

How to show the series of expectations for truncated symmetric random variables is convergent

Suppose that $(X_n)$ is i.i.d. with symmetric distribution and that $E(|X_1|)<\infty$. I want to show that $\sum\limits_{i=1}^{\infty} \frac1iE(X_i 1_{[|X_i|<i]}) $ converges. Attempt: Since ...
1
vote
1answer
15 views

Sampling distribution question with unknown n.

Suppose that 53% of the population of voters were in favor of fighting the global warming. If we wanted to conduct a random sample of size $n$ of voters, how many should I survey if I want the ...
5
votes
0answers
52 views

Random Walk Without Repetitions

Suppose that we simulated a random walk on $\mathbb Z$ starting at $0$. At each step, we transition from position $x$ to position $x-3,\,x-2,\,x-1,\,x+1,\,x+2,$ or $x+3$ with equal probability. If ...
0
votes
1answer
14 views

Rescaling a probability

I can't ge me head around this. I know that between 00:00h and 00:30h (i.e. within 30 minutes) a person is with a chance of 90% in room A, 7% in room B and 3% in room C. Now the task is, to derive a ...
0
votes
0answers
17 views

Mean and variance question

An electronic device periodically records the voltage applied at its input, truncating it to the nearest integer in each case. Under the usual assumptions, evaluate the mean and variance of the error ...
1
vote
3answers
27 views

Finding the probability of an event with binomial distribution using a normal approximation

A Tarheels basketball player is obsessed about practicing his free throws. It is known that he is $75\%$ free throw shooter. One morning he decides to shoot $100$ free throws. You may assume that ...
1
vote
1answer
30 views

probability over 3 values with dependency

At the exercise, there is no information that B and C are independent, but with logical reasoning, there must be a pendency. The problem is, I can not create a connection with depency of B and C, is ...
1
vote
0answers
10 views

UMVUE for altered Normal distribution

Let $X_1 , ...,X_n$ be a sample from a normal population $N(\mu , \sigma^2)$. It's easy to find the UMVUE for $\mu$ and $\sigma^2$: (1) After finding the joint density of X=$(X_1 ,...,X_n)$, we find ...
4
votes
0answers
19 views

Analysis of sorting Algorithm with probably wrong comparator?

It is an interesting question from an Interview, I failed it. An array has n different elements [A1 .. A2 .... An](random order). We have a comparator C, but it has a probability p to return correct ...
-2
votes
0answers
15 views

Identifying markov chains and the markov property [on hold]

Im currently revising for a probability exam and I came across this question: Let $(X_n),n\geq1$ be a sequence of independent identically distributed non- negative random variables taking values in ...
2
votes
0answers
26 views

How to show that $p(t|x,\mathbf x,\mathbf t)= \int p(t|x,\mathbf w)p(\mathbf w|\mathbf x, \mathbf t)d\mathbf w $

The following paragraph is approximately cited from Bishop's book, Pattern Recognition and Machine Learning. In curve fitting problem, we have training data $\mathbf x$ and $\mathbf t$, along ...
0
votes
0answers
18 views

expectation approximation

Note: You don't have to understand Approximation Algorithms to answer this Hello. I need to prove an algorithm approximation by using expectation. The algorithm takes $x_i \in {0,1,2}$ such that ...
-2
votes
0answers
32 views

I need help to solve this complex question [duplicate]

Peter has 12 pairs of socks and 6 pairs of gloves in different colors. His socks are in green, yellow, black, and grey (3 pairs each). Peter's gloves are either blue, black, or red (2 pairs each). ...
0
votes
2answers
39 views

Tricky Cardinality Question/Riddle [on hold]

Mike is a child and he is playing with lego box. He begins by counting the number of pieces in his lego box. He recognize that some pieces are green, some pieces are blue, and some are green and blue. ...
0
votes
0answers
11 views

Under what assumptions is the following first moment monotone?

I'm working on an economic model and am encountering the following mathematical issue. Let $x\sim \mathcal{N}(\mu,1)$, and define $$V(\mu)=\int_0^{\hat x(\mu)}x ...
-1
votes
2answers
39 views

Can anybody help me to solve this counting problem [on hold]

A color on screens is the result of a combination of three colors red (r), blue (b), and green (g). A color c can be represented by the formula $$c = p_rr + p_bb + p_gg$$ where $$0 ≤ p_r, p_b, p_g ...
0
votes
1answer
50 views

Compute Var(x=X1+X2+…+Xn)

Compute $Var(X_1+X_2+...+X_n)$ given $X_1,X_2...$ are iid.,$EX=\mu,Var(X)=\sigma ^2$,and $Var(N)=\sigma [n]^2$, N is a random variable of nonnegative integers independent with X, and my solution ...
2
votes
1answer
48 views

Probability of asymmetric random walk returning to the origin

Consider the random walk $S_n$ given by $ S_{n+1} = \left\{ \begin{array}{lr} S_n+2 & with & probability & p\\ S_n - 1 & with & probability & 1-p \end{array} ...
2
votes
1answer
23 views

Uniformly Distributed random varibles

Question:Suppose $X$ is a uniformly distributed random variable with possible values $1,2, \ldots, 10$. Compute the expected value and variance of $X$. I have started with making a column ($x$ on the ...
-4
votes
1answer
17 views

Find the 95% confidence interval and interpret the results [on hold]

A random sample of 38 200-meter swims has a mean of 3.96 minutes and the population standard deviation is 0.06 minutes. Construct a 95% confidence interval for the population mean time. Interpret the ...
2
votes
1answer
21 views

Expected value for sum of iid normal variables squared

Let $X_i$ be iid from a $N(\alpha, \alpha)$ distribution. I am trying to find $E[\sum_1^n X_i ^2]$ and thought that I would be able to transform the statistic $\sum_1^n X_i ^2$ into a chi-squared ...
1
vote
0answers
23 views

Joint Probability Question

I have a question regarding join distributions. For this question, I have to find the probability that P(X+Y=0). I've attempted multiple different ways to solve this problem, but I keep getting 0 as ...
1
vote
1answer
17 views

Covariance and Correlation in Multinormal random variable

Find the covariance and correlation of $N_i$ and $N_j$, where $N_1, N_2, \ldots,N_r$ are multinormal random variable. At the beginning, I think that I have: ...
0
votes
0answers
8 views

Lists of common sufficient statistics

Can someone suggest a source for common sufficient statistics for exponential families? For example, I'm looking for something more comprehensive than the Wikipedia page for sufficient statistics, ...