Tagged Questions

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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Probability of walking into a pole

I have a problem I am thinking about...someone posted on Facebook about randomly walking into a pole and it got me thinking. Say there is a straight line of 100 metres, and in that straight line is ...
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Is truncating a discrete probability mass function possible?

I have random variable X, and probability distribution: $P[X = A] = .4$ $P[X = B] = .3$ $P[X = C] = .2$ $P[X = D] = .1$ I want to create a conditional probability with event F. Where F is the ...
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Identify the sample points in the events $A \cup B$

A pair of fair dice is tossed. Events $A$ and $B$ are defined as follows : $A$: (The sum of the numbers on the dice is $3$) $B$: (At least one of the dice shows a $2$) Identify the sample points in ...
361 views

Selecting groups of items: How many ways can we divide n students into groups of two?

I have a question very similar to the post in the link below. But, what do we do when we are given a variable for the total number of students, not a constant number? Here is the modified version of ...
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Is $\theta_1-\theta_2$ independent of $\theta_1-\theta_3$ given all are uniform random variables between $[-\pi,\pi]$

I have three random variables $\theta_1, \theta_2, \theta_3$ all are i.i.d uniformly over $[-\pi,\pi]$. These in reality represent angles in my problem that I am trying to solve. I have a linear ...
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There are $N$ coins placed in a line. A coin may be facing head/tail direction with $0.5$ probability. Now I need to find number of pairs of coins $(i,j)$ such that $i<j$ and on index $i$ , I ...
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Probability of picking balls out of bins

Question: You have two bins with four different balls in each bin. Bin A: 2 White Balls and 2 Black Balls Bin B: 3 Black Balls and 1 White ball You cannot tell which bin contains what balls. Given ...
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Finding the probability of exactly one event in a series of independent events, why used (-1)?

Learning programming and trying to understand this example. Given multiple independent events, each with a probability of occurring, what is the probability of just one event occurring? If we have ...
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When does pairwise independence imply independence?

We know if a collection of events are independent, then they are pairwise independent. In general, the converse is not true. However, I'm wondering if there's a condition under which the converse ...
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Determining a consistent estimator/asymptotic relative efficiency

Question: Let $X_1,\ldots,X_n$ be i.i.d. as $N(0,\sigma^2)$. a) Show that $\delta_1 = k \sum_{i=1}^n |X_i|/n$ is a consistent estimator of $\sigma$ if and only if $k = \sqrt{\pi/2}$. b) Determine ...
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Matching moments implies matching densities?

If $X$ and $Y$ are random variables with matching moments (ie: $\mu_X^i = \mu_Y^i (\forall i \in \mathbb{Z}^+)$ then are the density functions of $X$ and $Y$ identical (almost everywhere)? Idea: I'm ...
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I am trying to show that if $X(\omega) = \infty \space\forall \omega \in A$, $P(A) > 0$ and $X \ge 0$ then $EX = \infty$. The problem comes with a hint: $$EX = E\{X[I(A) + I(A^c)]\} = E[XI(A)] +... 3answers 225 views Probability of the horse winning, given the chance of rain Here's the question: In the past two racing seasons Seahorse has won 55% of the time if the track is dry. On rainy days when the track is muddy he won only 30% of the time. For the next ... 3answers 62 views Probability and counting cards The problem goes like this: "I am given 7 cards from a regular 52 playing card deck." "Find the probability that there are at least 3 of the cards equally high (e.g. that there are 3 or more jacks). ... 3answers 230 views Probability with colored flags A signal has 6 flags, each flag can be blue, white or red. Possible signals formed is n^r = 3^6 = 729 possible signals formed How many different signal can be made from 6 flags of which 3 ... 3answers 2k views round table seating probability There are 6 people, let's call them - (a,b,c,d,e,f), to sit at a round table. The number of ways they can arrange themselves is (6-1)! = 5! = 120 ways. What is the probability that person 'a' ... 1answer 35 views Expression of the thresold with expected degree in a Random Geometric Graph n points (P_i) are distributed uniformly on the surface of an unit radius sphere. 2 points are interconnected if the distance between them is \le r (thresold). We call the degree of point i (... 1answer 59 views Binomial distribution for a poll I'm looking for help with this question on the binomial distribution. ... 1answer 88 views Conditional Integral of Square of Brownian Motion? I am struggling to compute the expectation and variance of the following, where W(s) is a standard Brownian motion:$$ X := \int_{0}^{A}W(s)^2ds Y:= \int_0^AW(s)ds E[X\mid Y] = \space ?$$... 1answer 220 views Dirichlet distribution, sum of Beta distributions I currently have a problem about Dirichlet distributed Variables. In one of the papers I am currently reading it says: Let S=(S_1,...,S_m)\sim Dir(\delta\omega_1,..., \delta \omega_m), with \sum_{... 2answers 22 views Probability of number drawing The number 1,2,3,4 are written on slips of paper and 2 slips are drawn at random one at a time without replacement. What is the probability the first number is 2 or the sum is 5? 1answer 44 views How do I find E[X_1|X_1<X_2] when X_1 and X_2 are independent N(0,1) random variables? [closed] What property of Gaussians do I have to exploit to solve this? 0answers 101 views Binomial Distribution/ Law of large numbers I currently have the problem to establish that  \underset{n \rightarrow \infty}{\lim} \sum_{k=0}^{\lfloor n\cdot l\rfloor} \binom{n}{k} (s)^k(1-s)^{n-k} = \begin{cases} 0, & \text{wenn}~l< ... 1answer 92 views A probability problem, Maximum likelihood or Bayesian updating? I see an interesting probability problem: Suppose you were playing table tennis with A, you did not know the strength of A. Since the start, A had won 3 scores consecutively. What was the ... 1answer 26 views Probability of a Brownian Motion to fall in a bandwidth Let X_t be defined as$$ X_t = X_0+\int_0^t\sigma_{0}\,dW_s, $$where W_s is a Wiener process and \sigma_0\in\mathbb{R}^{+}/{0}. Which is the probability$$ \mathbb{P}\left[a<X_t-X_0<b\...
Suppose $X$ is a random variable. In most undergraduate math texts, one writes the expected value of $X$ as $\text{E}X$ or $\text{E}[X]$. Similarly, the probability that $X$ is greater than some value ...