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 ...

learn more… | top users | synonyms (2)

0
votes
0answers
2 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 ...
0
votes
1answer
6 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. ...
0
votes
1answer
23 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 ...
0
votes
1answer
16 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.
1
vote
3answers
2k views

How to use stars and bars(combinatorics)

How to use the stars and bars method? Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$ Where $x_i\in\mathbb{N}$ Is this the correct time to apply the method?
2
votes
2answers
35 views

Probability of a pair of red and a pair of white socks among five chosen

In the box are $7$ white socks, $5$ red socks and $3$ black socks. $2$ socks are considered a pair if they have the same color. $5$ arbitrary socks are selected at random from the box. ...
0
votes
1answer
23 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. ...
1
vote
1answer
15 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 ...
0
votes
0answers
17 views

Convert min to max probability

Assuming $Y=min(q_1,\ldots,q_n)$ , $q_i\sim N(\mu,\sigma^2)$ I want to express $Y$ in terms of the $Q$ function. Knowing that $Y=min(q_1,\ldots,q_n)=-max(-q_1,\ldots,-q_n)$ $P(Y\leq y)= ...
0
votes
0answers
11 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 ...
0
votes
0answers
10 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
11 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
8 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 ...
11
votes
2answers
166 views

Using probability methods prove $\frac{\sin(t)}{t} = \prod_{i=1}^{\infty} \cos \left( \frac{t}{2^i}\right )$

Using probability methods (characteristic function?) prove $$\frac{\sin(t)}{t} = \prod_{i=1}^{\infty} \cos \left( \frac{t}{2^i} \right)$$ I know what is characteristic function but I have no idea ...
0
votes
0answers
20 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 ...
2
votes
0answers
27 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 ...
1
vote
2answers
45 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 ...
1
vote
0answers
29 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 ...
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
1answer
32 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?
-3
votes
0answers
21 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
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
votes
0answers
14 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
0answers
51 views

A function with a bijection

Let $r:\Bbb N^*\to\Bbb Q$ a bijection and $r_n=r(n),\forall n\in\Bbb N^*$. $f_r$ is the function such that: $$\forall x \in \Bbb R, f_r(x)=\sum_{n\in I_x} \frac{1}{n(n+1)}$$ where $$I_x=\{n \in \Bbb ...
-2
votes
0answers
34 views

Inequality with poisson r.v. [on hold]

Let $r>0$ and $X \sim Poisson(\lambda)$. Prove that ( $e=2.71...$) $$ \mathbb{E} X^r \le r^r + (e \cdot \lambda)^r $$ I can show it for $r \in \mathbb{N}$ by writing expected value as series, ...
2
votes
2answers
68 views

Two people meeting, expected time of waiting

$A$ and $B$ are supposed to meet. $A$ arrives in a randomly chosen (uniform distribution) moment between $2$ and $3$ pm. $ B$ arrives at $2$ pm with probability equal to $0,5$ and in a randomly ...
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 ...
7
votes
2answers
687 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 ...
1
vote
0answers
17 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 ...
2
votes
1answer
421 views

Random walk, Cat and mouse

Here is the problem. In graph G, on different vertices there is cat and mouse. Cat and mouse do independent random walk, but time is synchronous, in one unit of time both cat and mouse do one step. ...
0
votes
2answers
34 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
1answer
1k views

Finding joint cdf and pdf of independent random variables

Let $X$ and $Y$ be independent random variables. Each has an exponential distribution with parameter $\lambda$. Define two new random variables by $W = \min({X,Y}) $ $Z = \max({X,Y})$ Find the ...
1
vote
0answers
36 views

Weak convergence of a sequence of cdfs

Suppose $F_n \to F $ weakly, $ x \in c(F)$ and $ x_n $ is a real sequence converging to x. Prove that $F_n(x_n) \to F(x) $. Here $F_n$, $F$ are cdfs and $c(F)$-set of continuity points of $F$. I ...
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 ...
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
1answer
22 views

Statistics - Mean value and net revenue

From the following book:Probability and Statistics for Engineering and Science
0
votes
1answer
24 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 ...
0
votes
0answers
13 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 ...
-4
votes
0answers
18 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?
-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. $X(t) = exp[(\mu - 0.5\cdot \sigma^2)t + \sigma\cdot W(t)]$ ...
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 ...
0
votes
3answers
167 views

In a bit string of length 11, how do you find the probability of even number of zeros?

I thought about doing the complement but I wasn't sure if that was correct. Or add up the different cases that there is an even number of 0's as the probability?
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 ...
-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
1answer
38 views

Mean return time in Markov chain

Given the following Markov chain: $p_{0,1}=1$ (if we are in state 0, we must go to state 1) $p_{i,i+1}=p_{i,i-1}=0.5$ There are infinitely (countably) many states. I assume that $X_0=0$ and define ...
1
vote
1answer
16 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 ...
2
votes
1answer
52 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} ...
5
votes
0answers
54 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 ...
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
31 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 ...