Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [conditional-probability]

In probability, conditional probability, is the probability that an event occurs given something else has already occurred.

0
votes
1answer
17 views

Probability of specific card being in the deck vs your players hand?

If there are 7 cards left in a deck of cards, and 5 cards in the other players hand and you've seen all the cards except for the following: Spades: ♠ 10 K Hearts:♥ 10 Q K A Clubs: ♣ 10 J Q K A ...
1
vote
0answers
18 views

Multivariate Conditional Entropy as a test of correlation between random variables

I use the word columns to mean the data from which a random variable can be estimated. It is a sample of a random variable. I am working with $N$ columns of weakly correlated data. Furthermore, I ...
0
votes
1answer
38 views

How does the knowledge of one's preference for A over B affect the probability of one's preference for C over B if one's preference is transitive?

Suppose you know someone has preferences between the three pizza toppings pepperoni, olives and mushrooms. If you are told that they prefer pepperoni over olives then what is the probability that ...
0
votes
1answer
31 views

Conditional probability of $X$ being even given joint pmf $f_{XY}$

I want to calculate: $$ \mathbb{P}[ 2Y = 3X ~\vert~ \text{$X$ is even} ]$$ given this joint pmf: $$ \mathbb{P}(X = k, Y = n) = e^{-2} \frac{(1-e^{-1})^k}{(n-k)!}$$ From the joint I found the ...
-2
votes
1answer
40 views

What is the probability that heads or tails shows twice in a row exactly once in the ten coin tosses [on hold]

What is the probability that heads or tails shows twice in a row exactly once in the ten coin tosses. I also want to understand the process followed to achieve it.
-2
votes
1answer
31 views

What is the probability that in 10 coin tosses head never follows head and tail never follows tails [on hold]

I just want to learn the probability that in 10 coin tosses head never follows head and tail never follows tails. Also I want to understand the process by which the result is achieved.
0
votes
1answer
34 views

Conditional variance when there is uncertainity about the distribution of condition

Assume that $X \sim N(0,\sigma_x^2)$. Y has the following form \begin{align} Y &= \begin{cases} Y_1 \sim N(0, \sigma_1^2), & \text{w.p.} \quad \mu \\ Y_2 \sim N(0, \sigma_2^2), & \text{w....
1
vote
1answer
31 views

Probability of union using conditional probabilities

I'm struggling trying to calculate the probabilities associated with a random variable $Z$ whose value depends on the realizations of two other random variables $X,Y$. I have : $$ Pr(X=A)=0.25, Pr(Y=...
0
votes
0answers
17 views

Truncated conditional expectation of multivariate normal distribution

Assume that $y_1 = \alpha_1 s_1 + u_1$ and $y_2 = \alpha_2 s_1 + \alpha_3 s_2 + \alpha_4 u_1 + \alpha_5 u_2$ where $s_1 \sim N(0,\Sigma_1)$, $s_2 \sim N(0,\Sigma_2)$, $u_1 \sim N(0,\sigma^2)$, $u_2 \...
1
vote
1answer
24 views

Using Bayes Law leads me to a seemingly nonsensical result

I am trying to prove that, given events $A$ and $B$, if $P(A) > P(B) > 0$, then $P(A|B) > P(B|A)$ Now, here is my proof: $P(A|B) = \dfrac{P(A)P(A|B)}{P(B)} \tag*{(by Bayes' Theorem)}$ $P(...
0
votes
1answer
13 views

Determine Computability of Joint and Conditional Probabilities Given Few Tables

Problem I've encountered the following problem during the introduction lecture of my Machine Learning class. I haven't taken a formal probability course yet, so any help would be appreciated. ...
1
vote
1answer
26 views

Donkey hitting his head on the same stone - a question about probability

I am practising for an exam that has a section on introductory probability theory, we have covered basic Markov chains and conditional probability + binomial distribution, not much more. In these ...
0
votes
1answer
19 views

The conditional expected value of a two-dimensional variable

I have problem: We have two-dimensional variable: ($X,$Y), which has density: $$ f(x,y) = \left\{ \begin{array}{ll} 2x^2 & \textrm{when $-1<x<1$ and 0<y<|x|}\\ 0 & \textrm{in ...
1
vote
0answers
28 views

Clarifications on the definition of $P(\cdot|X=x, Y\neq y)$?

I have a question on the following: take two random variables $Y,X$ with support $\mathcal{Y}, \mathcal{X}$ respectively. Let $y\in \mathcal{Y}$, $x\in \mathcal{X}$. Let $P(\cdot | X=x)$ be the ...
0
votes
0answers
11 views

Conditional probability of Negative Binomial R.V. given the SUM of its values

Suppose $\{z_{ij}\}$ are independent Negative Binomial random variables with means $\{\mu_{ij}\}$, with $i=1\dots I$ and $j=1\dots J$. How do you find the (expectation of) conditional probability ...
0
votes
0answers
24 views

Show that sum of these two Random Variables is conditionally normal distributed (from IGARCH model)

According to Tsay's book (Analysis of Financial Time Series) in Chapter 7, for the Risk Metrics model, the following sum, $r_{t+1} + r_{t+2}$, should be conditionally normal distributed. $σ_t^2 = ...
0
votes
2answers
175 views

~Conditional Probability~ rate(A|B) and rate(not A|B)

Example if: rate(A | B) = 10/180 x 100% ≈ 6%, rate(not A | B) = 170/180 x 100% ≈ 94% Since rate(A | B) < rate(not A | B), is there association between A and B ...
1
vote
1answer
23 views

Are these numbers sufficient for calculating $P(\alpha|\beta,\gamma)$?

Given three probabilities $Pr(\beta|\alpha)$, $Pr(\gamma|\alpha)$ and $Pr(\alpha)$; and that $\beta$ and $\gamma$ are conditionally independent given $\alpha$, can $Pr(\alpha|\beta, \gamma)$ be ...
0
votes
1answer
37 views

Finding the probability of fair coin [closed]

A hat contains 100 coins, where at least 99 are fair, but there may be one that is double-headed (always landing Heads); if there is no such coin, then all 100 are fair. Let D be the event that ...
2
votes
1answer
58 views

What is the probability that after removing all red balls, you have exactly 1 blue and at least 1 green ball remaining?

You have a box with 10 red, 20 blue, and 30 green balls. You take out balls from the box, without returning them. What is the probability that after you've taken out the last red ball there is ...
0
votes
1answer
16 views

Conditional probability of continuous random variable

I understand that the formula for calculating a conditional probability is the following $P(A \mid B) = \frac{P(A \cap B)}{P(A)}$ I have this probability to calculate: $P(2\le X \le 3 \mid X \ge1)$. ...
-3
votes
0answers
22 views

What is the probability of next person has ace of diamond given that you don't have it [closed]

4 people draw 2 deck of cards. What is the probability of the person next to you have at least 1 ace of diamond(2 ace of diamond in the entire deck) given that you don't have any. Also what is the ...
0
votes
0answers
20 views

Modelling conditional distribution based on multiple variables of various types?

I have a looking basic statistics problem: basing on a large sample of multivariate data, model conditional probability distribution (continuous) of one variable based on the remaining ones: a few ...
0
votes
0answers
21 views

adapted, increasing, (locally) integrable variation process is a (local) submartingale

I read a theorem that an adapted, increasing, (locally) integrable integrable, variation process is a (local) submartingale. (here increasing includes right continuity). Definition: A process is $\...
0
votes
0answers
45 views

Let $M$ ~ $Geometric(p)$ and $X \vert M = m$ ~ Uniform on integers 1…m

Let $M$ ~ $Geometric(p)$ and $X _{\vert M = m}$ ~ Uniform on integers 1....m. I want to find the density of X and its expected value. This is what I have done so far, but I am not sure it is right: ...
0
votes
0answers
18 views

calculating Probability and prediction.

I am trying to calculate the probability for admission to a restaurant, in foot forward to have a rough idea to predict how many admissions would be there in 5 years from now. The question is: is 18 ...
-1
votes
0answers
17 views

How to describe sigma algebra for both conditional and unconditional probabilities

This question is not about random variables and stochastic processes, I'm talking about 101 Kolmagorov Probability definitions. I have a problem with determining a correct probability space for this ...
1
vote
1answer
32 views

How to drive the CDF of random variable $Z$ define by $ Z=\frac{X_iX_j}{2X_i+X_j} $

I am working in wireless communication and some times we use the PDFs and CDFs of random variables. So I have read a paper and I found the derivation of CDF and PDF of random variable, but I did not ...
2
votes
2answers
59 views

What is the distribution of $X|W=w$?

Let $X$ and $Y$ be independent random variables with uniform distribution between $0$ and $1$, that is, have joint density $f_{xy}(x, y) = 1$, if x $\in$ $[0,1]$ and y $\in [0,1]$ and $f_{xy} (x, y) = ...
0
votes
1answer
30 views

Three cities, four roads, one railway: a probabilistic traveling problem

Two roads join Ayton to Beaton, and two further roads join Beaton to the City. Ayton is directly connected to the City by a railway. All four roads and the railway are each independently blocked by ...
2
votes
1answer
33 views

Dick throws a die once. If the upper face shows $j$, he then throws it a further $j−1$ times and adds all $j$ scores shown. If this sum is $3$ . . .

Dick throws a die once. If the upper face shows $j$, he then throws it a further $j − 1$ times and adds all $j$ scores shown. If this sum is $3$, what is the probability that he only threw the die (a)...
0
votes
0answers
33 views

You roll two fair dice. What is the probability to win the game based on restrictions over the sum of the results?

You roll two fair dice. If the sum of the numbers shown is $7$ or $11$, you win; if it is $2$, $3$, or $12$, you lose. If it is any other number $j$, you continue to roll two dice until the sum is $j$ ...
-1
votes
0answers
17 views

Is my results true in Conditional probability?

I'm new in Conditional probability, Is my results true?? if we have $\text{Universal Set}= \{1,2,3,...,100\}$, $A=\{1,2,3,...,20\}, B=\{1,2,3,...,8\}, C=\{9,10,11\}$ . $P(A)= \frac{20}{100}$, $P(B)=...
-4
votes
0answers
33 views

Finding probability of 5staples in a stapler [on hold]

An office employee has TWO staplers on his table, one purple and another green. Each time he needs to staple two documents, he is equally likely to choose either of the purple or green staplers. ...
2
votes
2answers
43 views

What is the probability that no cup is on a saucer of the same colour?

A tea set comprises four cups and saucers in four distinct colours. If the cups are placed at random on the saucers, what is the probability that no cup is on a saucer of the same colour? MY ATTEMPT ...
0
votes
0answers
17 views

How to represent conditional distribution of a given Markov Chain?

Let $\mathbf{X} = (X_1,\dots, X_n) \sim P_{\mathbf{X}}$ be i.i.d samples and $\mathbf{x}:=(x_1,\dots, x_n)$ be its realizations, respectively. Let $T:= t(\mathbf{X})$ be a statistic, where $t(\cdot)$...
0
votes
1answer
20 views

Summation over an Event given Conditional Probability

Consider two events $G$, $A \in E(\Omega)$, where $E(\Omega)$ is an event space. Consider P(G|A) is the posterior probability distribution over $G$. Now if you sum over $G$, then why is it equal to $...
1
vote
1answer
73 views

Show that $\max\{\textbf{P}((A\cup B)^{c}),\textbf{P}(A\cap B),\textbf{P}(A\triangle B)\}\geq\frac{4}{9}$

Let $A$ and $B$ be independent events. Show that \begin{align*} \max\{\textbf{P}((A\cup B)^{c}),\textbf{P}(A\cap B),\textbf{P}(A\triangle B)\}\geq\frac{4}{9} \end{align*} MY ATTEMPT Since $\textbf{P}...
1
vote
0answers
32 views

Show that two processes have the same distribution knowing that their paths up to time $τ$ and their distributions conditioned on $\mathcal F_τ$ agree

Let $(\Omega,\mathcal A,\operatorname P)$ be a probability space $(E,\mathcal E)$ be a measurable space $(Y_n)_{n\in\mathbb N_0}$ and $(\tilde Y_n)_{n\in\mathbb N_0}$ be time-homogeneous Markov ...
0
votes
2answers
28 views

Should I use conditional probability/prior probability here?

I have been debating the following problem with my friends over the past few days: “I'm going on a holiday to Mumbai. I'm curious about the weather there so I call my friend who lives there and ask ...
0
votes
2answers
37 views

Four red balls and two blue balls are placed at random into two urns so that each urn contains three balls

Four red balls and two blue balls are placed at random into two urns so that each urn contains three balls. What is the probability of getting a blue ball if (a) You select a ball at random from the ...
2
votes
0answers
25 views

What can we say about a regular version of the conditional distribution given a random variable $X$ on the set $\left\{X=x\right\}$?

Let $(\Omega,\mathcal A,\operatorname P)$ be a probability space $(E_i,\mathcal E_i)$ be a measurable space $X_i:\Omega\to E_i$ Assume $X_2$ is $(\mathcal A,\mathcal E_2)$-measurable and that there ...
0
votes
0answers
29 views

Pick 5 numbers - calculate probability that respective 4-number combinations appear for $n-th$ time (given probability for their $n-th$ time)?

We pick 5 unique (distinct) numbers out of [1..36] numbers (like playing a lottery). Each time we pick 5 unique numbers ("play one ticket") thus we select 5 distinct combinations of 4 numbers out of ...
1
vote
0answers
21 views

Integral of multivariate probability function divided by its marginal?

I do not know how properly establish the problem in words, I will show it in equations. $$ \int f_{Y|X}(y|x) dx = \int \frac{f_{X,Y}(x,y)}{f_X(x)} dx $$ where $ f_{Y|X}(y|x) $ is conditional ...
0
votes
1answer
19 views

Conditional probability with choosing two cards from a deck

Two cards are picked randomly from a deck. What is the probability that if the first card is Spades, the second card will be a Queen? What I have so far: Let $A$ be the event the first card is ...
1
vote
1answer
48 views

What is the conditional probability density function of a statistic given its samples?

I want to find a probability density function (pdf) of a statistic $T:=t(X_1,\dots, X_n)$ given its samples $(X_1,\dots, X_n)=: \mathbf{X}$, where $t(\cdot)$ is a function such as $t(x_1,\dots, x_n)...
0
votes
1answer
32 views

Probability of two aces when we get at least one ace

"In drawing two cards from a deck (without returning the first card) what is the probability of two aces when you get at least one ace?" I am aware there is exact same question answered here. ...
1
vote
1answer
39 views

What is the expected value from these two different coin tossing games?

Consider these two games: Game $1$: Toss $4$ coins. If coins $1$ and $2$ are heads, you win $\$5$. If coins $3$ and $4$ are heads, you win an additional $\$5$. Game $2$: Toss $3$ coins. If coins $...
0
votes
1answer
30 views

Does a zero conditional expectation imply pairwise covariance is 0?

Suppose in econometrics, $$ y = \beta_{0} + \beta_{1}x_{1} + \beta_{2}x_{2} + ... + \beta_{k}x_{k} + u$$ In Gujarati's book, it says that the following equation (1) $$ E[u | x_{1}, x_{2},..., x_{k}] = ...
0
votes
1answer
40 views

Finding $Var(X)$ from conditional PDF

Let $X$ and $Y$ be random variables such that $X \vert Y=y$ is normal distributed as $N(y,1)$ and Y is a continues random variable with PDF: $f_Y(y)=3y^2$ for $0<y<1$ and $0$ otherwise. ...