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Questions tagged [probability]

For basic questions about probability and for questions about calculating a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using [tag:measure theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

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639 views

Monty Hall Problem-Probability Paradox

I just learned about the Monty Hall Problem and it seemed pretty much amazing to me.I am just a bit confused with it. So,according to the problem we are on a game show, and we are given the choice of ...
0
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2answers
23 views

Having a problem on a paradoxical answer

Suppose that we have PN objects (disks for an example) and we have P slots (or boxes),how many ways can we distribute those PN objects on those P slots so that each slot has exactly N object? i saw a ...
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0answers
17 views

Do jumps in Levy processes need to be independent of the process itself?

I have a very basic question about Levy processes. Is the process of the form $$ X_t=\sigma (X_t) B_t + \sum_{i=1}^{N_t}\eta_i(X_t) $$ a Levy process? Here $B_t$ is a standard Brownian motion and $N_t$...
5
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3answers
676 views

Counting process which is not a Poisson process

Please construct a counting process N, whose r.v. N(t) are distributed as Poisson(λt) but the process N itself is not a Poisson process. This is an assignment in our Stochastic Process class. So I ...
0
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1answer
32 views

How do you determine if a pair of random variables are independent?

If $A$ is a subset of $R$ and $X$ is a random variable. I have two variables $X_1$ and $X_2$. $I$ being $1$ if $X$ in subset $A$ and $0$ if not in $A$. Let $U$~$U(0;1)$ and determine if this pair ...
2
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3answers
530 views

Expected Entropy Based on Dirichlet Distribution

The Dirichlet Distribution basically defines the probability that a sample came from a particular multinomial distribution if we assume that the prior probability of all multinomial distributions ...
0
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1answer
24 views

Bayes Formula for more than 2 events

I have the following result used in one of the paper that I'm reading. I can't seem to get around how it is derived. Please help. $$ P(M\mid D,R) = \dfrac{P(M\mid R)\,P(D\mid M)}{P(M\mid R)\,P(D\mid ...
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3answers
27 views

Probability after a specific sequence of events?

I am working on some probability problems (not homework, I'm actually a 24 year old software developer who is doing some number crunching for a personal project) and wondering if someone who ...
1
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1answer
31 views

Probability of getting from one point to another given probability that path is open

The points Woodstock and Tunbridge (W and T) are connected above in 3 different scenarios. p and q are the probability that the path is open. The question is what is the probability one can get from W ...
0
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0answers
26 views

Why is $ P(−y ≤ X ≤ y) = 2P(0 ≤ X ≤ y)$ and not just $P(0 ≤ X ≤ y)$ when the range of $y$ is $[0, ∞)$

Given that $Y=|X|$ , the range of $y$ is $[0, ∞)$, $P(Y ≤ y) = P(−y ≤ X ≤ y) = 2P(0 ≤ X ≤ y)$ My question is, why does $ P(−y ≤ X ≤ y)$ equal to $2P(0 ≤ X ≤ y)$ and not just $P(0 ≤ X ≤ y)$ ? ...
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1answer
54 views

Cutting a rope randomly and taking the longer piece, cutting the longer piece and taking the shorter piece.

Cut a rope with unit length into two pieces randomly. Cut the longer piece of the first cut into two randomly again. Take the shorter piece from that second cut. What would be the PDF and the expected ...
0
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1answer
18 views

A randomly selected number between 1 and 5

How come $f_X (x)$ is not equal to 1/5? Because it should be $f_X (x) = 1/x$ so $f_X (x) = 1/5$ because x is defined on [1,5] right?
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2answers
19 views

Poisson Random Variable Question

A radioactive source emits certain particles with a Poisson distribution. The probability of no particle emissions during an hour of observation is $0.4$. What is the probability that the first ...
0
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2answers
56 views

Probability problem about a deck of cards.

Some cards were thrown away from a standard pack of $52$ cards. However all four aces were made sure to be kept among the remaining cards. Four cards were then selected at random from these ...
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0answers
9 views

transition semigroup and interpretation of excessive function

Let $\{P_t\}$ be a transition probability kernel. We say $f\in L^2(X)$ is a- excessive if for all $t>0$ and $x\in X$, it holds $e^{-at}P_tf(x)\leq f(x)$. My question: How can I interpret a-...
0
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1answer
21 views

let z1 and z2 be independent standard normal RV, find the pdf of $e^{3Z_1+2Z_2}$

Let Z1 and Z2 be independent standard normal random variables. Find the following The probability density function of $e^{3Z_1+2Z_2}$ The given solutions is as follows: But what doesn't make sense ...
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0answers
26 views

Density Function.

Let X be a random variable having density function as 𝑓(𝑥) = 𝑐 (1 − 𝑥) 𝑥 ;0 < 𝑥 < 1. Find the value of c. After solving this question I got the answer as 6, whereas the answer given in ...
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2answers
27 views

Cutting a 1 metre stick, what is the expected length?

I am unable to understand 2 things in this problem: Why is $f_X (x)$ = 1, should it not be 1/x because every point has the same chance of being cut. Does that mean every point has P=1 of being cut? ...
1
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1answer
42 views

Definition of a family of probability measures for Ito diffusions

I have a question concerning the definition of a family of probability measures for the solutions to an Ito diffusion $$X_t^x = x + \int_0^tb(X_s^x)ds + \int_0^t \sigma(X_s^x)dB_s$$ as it's given in ...
0
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1answer
9 views

For game where first player to N points wins, find the distribution of win probability and total number of points between players

Two players, A and B, play a series of points in a game with player A winning each point with probability p and player B winning each point with probability q = 1 - p. The first player to win N ...
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1answer
24 views

Maximum Variance of a Distribution

Let the random variable $X$ have the distribution $\mathbb{P}(X=0)=\mathbb{P}(X=2)$, $\mathbb{P}(X=1)=1-2p$ for $0\leq p \leq 1/2$. For what $p$ is the $\mathrm{Var}(X)$ maximum ?
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0answers
13 views

I am having trouble figuring out how many lambda's (births) there are in a given birth-death Markov process problem.

These questions are not for assignment. I am just confused as to how to set up the problem. I also do not need help calculating the problems at hand. I understand that in a birth and death problem, $...
0
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1answer
25 views

Combined probability distribution for two hazard functions

I have two items with two different failure rates. I need to find the combined hazard function corresponding to both items failing, from which I can find the combined probability distribution. I ...
0
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1answer
35 views

Why does $P(E) < P(F)$ imply that $E \subseteq F$?

Why does $P(E) < P(F)$ mean that $E \subseteq F$ ? My reasoning (using Venn diagrams): It is seen clearly in the below picture that even if $P(E)<P(F)$, there is still some region in E that is ...
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1answer
29 views

Probability of having drawn ace of spades after drawing a card and putting it back in the deck

I have been wondering if the probability of drawing a card from a 52 card deck, obviously 1/52 probability, is different from the following. If you get to draw a card from a 52 card deck and right ...
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1answer
61 views

Pdf of the product of an exponential rv and a $f_Y=Ka^{-K}y^{K-1}$ distributed rv …

Let $X$ and $Y$ are 2 independent random variables, where $X$ has an exponential distribution with parameter $1$ and $Y$ has the following Pdf: $f_Y=Ka^{-K}y^{K-1}, 0 \le y \le a $. Someone claims ...
2
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1answer
460 views

Finding meaningful differences in a set of time measures

An individual is presented with a list of words, one at a time, and asked to answer the first thing to comes to her mind. The delay of all answers is recorded. So I have a list of words, each paired ...
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0answers
35 views

drawing unique elements with replacement

I have a situation where I will draw a random number of balls from an urn with $r$ red balls and $b$ blue balls, with $N=r+b$. The number drawn is $k$, and I know the distribution $k$ comes from. ...
2
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2answers
40 views

Finding $E[X^2]$ for $X \sim Bin(25,0.61)$

I got something rather new and I just wanted to make sure my way of thinking in this field is fine. Suppose $$X\sim Bin(25,0.61)$$ and we are asked to find: $E[X^2]$. So basically I treat this ...
0
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1answer
16 views

given exponential Cumulative distribution function, finding another Cumulative distribution function with functionl connection

There is given $X$ a random variable with exponential cumulative distribution such that $X~Exp(1)$ so the exponential Cumulative distribution function is: $P(x\le t)= F_x(t)=(1-e^{-t} , 0\le t) \...
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0answers
19 views

Difference between two standard deviation formulas

I was just wondering about the difference between these two standard deviation formulas? I am extremely confused because with one of the standard deviation formulas, it also requires the standard ...
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1answer
29 views

Probability of a certain 5 card hand from a standard deck

A poker hand consists of 5 cards randomly dealt from a standard deck of cards without replacement. What is the probability that you're dealt a hand that contains exactly one pair of red Queens with ...
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1answer
29 views

How to solve this probability/combinatorics question about balls in bins

Below is the problem that I need to solve Suppose you blindly place five balls labeled A, B, C, D and E inside five bins labeled A, B, C, D and E. What are the chances that, in your selection, no ...
0
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1answer
45 views

Does MLE really care about PDF?

I am wondering, whether MLE really cares whether it operates on proper distributions. Lets take a look at the following situation: likelihood: $$L(\theta \mid x) = \prod_{n}^{N}{f(x_n \mid \theta)}$$ ...
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0answers
4 views

can you help me understand the inputs for this bayes theorem calculator for my scenario?

I'm trying to calculate the probability of delivering a website based on the conditional delivery of an underlying database. I entered some inputs into this online Bayes Theorem calculator: https://...
2
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1answer
7 views

Is counting partitions the same thing as counting permutations of set sizes?

I am looking at this formula As I understand it, this counts the number of ways you can a set into subsets of fixed sizes, assuming you use each element only one time. You can use this to calculate ...
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1answer
30 views

Different ways of computing probability

There are twelve unique watches and five men. Each of the five men are asked to choose a watch for themselves. What is the probability that at-least two of them choose the same watch. I could ...
0
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1answer
968 views

Consider a paint-drying situation in which drying time for a test specimen…

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with $\sigma = 8$. The hypotheses $H_0: \mu = 73$ and $H_a: \mu < 73$ are to be tested using a ...
0
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1answer
28 views

proof that $Y$ follows normal distribution

I'm new to probability and studying multivariate normal distribution. The one thing I don't understand is the linear transformation of multivariate normal distribution.If the $X$ follows Normal ...
3
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1answer
42 views

A game with an $n$-sided die

Suppose you play a game with a fair $n$ sided die (that, if being rolled yields us a discrete random variable uniformly distributed on $\{k \in \mathbb{N}| k \leq n\}$). You play the following ...
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1answer
1k views

Expected value of an estimator: biased estimator?

Let $f_X(x_i)=\theta\cdot x_i$, $x_i\leq \sqrt{2/\theta}$ with $\theta=\frac{2}{x_{(n)}^2}$ (derived using the MLE-method). What is the expectation of estimator $\hat\theta$? I'd assume that $\...
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0answers
22 views

A random variable formed by two Normal random variables, under a conditioning process.

Imagine two independent random variables, $X$ $\sim$ $N$ $(\mu_1$,$\sigma_1^2)$ and $Y$ $\sim$ $N$ $(\mu_2$,$\sigma_2^2)$. Now imagine a process whereby one observation of $X$ and one observation of $...
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0answers
35 views

Probability/ eggs in boxes

I have n boxes and n eggs, which were hidden randomly in these boxes. The probabilty, that no egg is in the right box, is $$ \sum_{k=2}^n (-1)^k \frac{1}{k!} $$ How can I get to this formula?
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1answer
25 views

How to understand this probability equation?

$\mathbf { x } ( t ) = g ( \mathbf { s } ( t ) ; \xi ) + \mathbf { n } ( t )$, where n(t) denotes the noise or modeling error and ξ the parameters of mapping $g$ How to understand the following ...
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0answers
29 views

Expected number of random rows needed to get a full-rank matrix

I have a random $m \times n$ matrix over $F_2$ of full rank (i.e. all columns are independent) where $m$ << $n$. Now, I wish to randomly choose $k$ rows such that the corresponding sub-matrix (...
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1answer
19 views

Joint Exponential Probability Problem

I have a question from A First Course in Probability by Sheldon Ross. Question: Consider two components and three types of shocks. A type 1 shock causes component 1 to fail, a type 2 shock causes ...
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1answer
27 views

Probability the event occurs knowing that I received no information

First I want to thank you if you pay attention to my post. I apologize if it seems elementary to you, note that I searched a lot an answer before posting. I'm going to try not to be vague, do not ...
2
votes
2answers
28k views

What is the probability of drawing 2 same colored marbles?

Suppose there are 3 colored marbles (Red, Blue, Green). There are 10 red, 20 blue, 30 green marbles. You select 2 marbles without replacement. What is the probability that they are the same colors? ...
2
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3answers
531 views

$\exp(-t^4)$ is not a characteristic function

I'm looking for the answer to the problem in the title. I know it comes from the Marcinkiewicz theorem, but I need formal proof of it.
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1answer
31 views

Probability in a comunication network

A communication network is made of nodes conected with wire. The net sends packets in such a way that if one packet is located in an internal node $x$ (internal node is the one connected to more than ...