In probability theory and statistics, given two jointly distributed random variables
X
{\displaystyle X}
and
Y
{\displaystyle Y}
, the conditional probability distribution of Y given X is the probability distribution of
Y
{\displaystyle Y}
when
X
{\displaystyle X}
is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value
x
{\displaystyle x}
of
X
{\displaystyle X}
as a parameter. When both
X
{\displaystyle X}
and
Y
{\displaystyle Y}
are categorical variables, a conditional probability table is typically used to represent the conditional probability. The conditional distribution contrasts with the marginal distribution of a random variable, which is its distribution without reference to the value of the other variable.
If the conditional distribution of
Y
{\displaystyle Y}
given
X
{\displaystyle X}
is a continuous distribution, then its probability density function is known as the conditional density function. The properties of a conditional distribution, such as the moments, are often referred to by corresponding names such as the conditional mean and conditional variance.
More generally, one can refer to the conditional distribution of a subset of a set of more than two variables; this conditional distribution is contingent on the values of all the remaining variables, and if more than one variable is included in the subset then this conditional distribution is the conditional joint distribution of the included variables.
My question relates to subsection 2.2.1 of [this article][1]. This subsection recalls the work of Lindgren, Rue, and Lindström (2011) on Gaussian Markov Random Fields (GMRFs). The subsection starts with a two-dimensional regular lattice where the 4 first-order neighbours of $u_{i,j}$ are...
Dear Everybody,
I am working on my homework. I am trying to prove a problem that was written by my professor in an odd way: Prove that when p is true, then q is true. Which proposition statement should I assume? I personally thought that I should assume the first one. But reading my...
So I am trying to do this tutorials but I want to use my own dataset. I am having problems "Build an input pipeline with tf.data."
My question is about their code:
def load_image_train(image_file):
input_image, real_image = load(image_file)
input_image, real_image =...
North and south have ten trumps between them ( trumps being cards of specified suit).
(a) Find the probability that all three remaining trumps are in the same hand. (that is either east or west has no trumps).
(b) If it is known that king of trumps is included among the three, what is the...
Problem: In a dresser there are 3 drawers. In one drawer there are two black socks and one white sock, in the second drawer there are two white socks, and in the third drawer there is a black and white sock. Suppose I chose a drawer randomly ( meaning, in a uniform distribution ) and I took a...
My attempt:
$$P(\text{B is positive}|\text{A is positive})=\frac{P(\text{B is positive} \cap \text{A is positive})}{P(\text{A is positive})}$$
$$=\frac{P(\text{B is positive})\times P(\text{A is positive})}{P(\text{A is positive})}$$
$$=P(\text{B is positive})$$
$$=0.01 \times 0.99 + 0.99 \times...
Hello,
I have a question about the following sentence and would appreciate if someone could explain how to read out the conditional probability here.
"Each microwave produced at factory A is defective with probability 0.05".
I understand the sentence as the intersection ##P(Defect \cap...
I've been reading a logic book and saw the logical statement below and have been trying to consider its meaning:
(∃x)(∀y) (Fyx ⊃ Fyy)
I keep going back and forth whether this statement is implying:
a) For all things, if they do F to x, then they do F to themselves
-OR-
b) If there's some x...
Hi,
If the events A and B are statically dependent then the following formulas are used to calculate conditional probability and joint probability but there is a problem. As I see it both formulas are dependent upon each other. One cannot calculate conditional probability without first...
We know that ##P(A-) = (95\% \cdot 0.5\% + 5\% \cdot 98.5\% )## and ##P(guilty \ and \ A-) = (95\% \cdot 0.5\%)##, so letter a) is just ##P(guilty \ and \ A-)/P(A-)##.
What I tried to do in letter b) was again using the conditional probability theorem. First calculating the probability that...
I'm just learning some basic predicate logic. I found this.
UD: People
Gx: x can play the guitar
l: Lemmy
In the expression ∃xGx→Gl, the scope of the quantifier ∃ is the expression Gx. This translates to If there is a guitarist, Lemmy is a guitarist.
Now this is changed to:
∃x (Gx→Gl), we...
Hi,
Just a quick question about conditional and marginal probabilities notation.
Question: What does ## p(a|b, c) ## mean?
Does it mean:
1) The probability of A, given (B and C) - i.e. ## p[A | (B \cap C)] ## OR
2) The probability of (A given B) and C - i.e. ## p[(A | B) \cap C] ##
I was...
Hi,
I have a quick question about something which I have read regarding the use of dirac delta functions to represent conditional pdfs. I have heard the word 'mask' thrown around, but I am not sure whether that is related or not.
The source I am reading from states:
p(x) = \lim_{\sigma \to...
I am trying to understand the following deduction:
"The conditional phase shift can be represented by the unitary operator 2|0> <0| - I:"
for eq. 4a) I was expecting to be:
[2 |0><0| - I] |0> =
2 |0> <0|0> - I|0> = 2|0> - |0> =
|0>
as for eq. 4b I can't understand it at all. Why does the...
Question
---
So I've done a calculation which seems to suggest if I combine the system of a measuring apparatus to say an experimenter who "reacts" to the outcome of the the measurement versus one who does not. Then the change in entropy in both these situations is bounded by:
$$ \Delta S_R...
Given an Exponentially Distributed Random Variable $X\sim \exp(1)$, I need to find $\mathbb{E}[P_v]$, where $P_v$ is given as:$$ P_v=
\left\{
\begin{array}{ll}
a\left(\frac{b}{1+\exp\left(-\bar \mu\frac{P_s X}{r^\alpha}+\varphi\right)}-1\right), & \text{if}\ \frac{P_s X}{r^\alpha}\geq P_a,\\
0...
Given that $X$ is exponentially distributed continuous random variable $X\sim \exp(1)$ and $g(x)$ is as below. How can I find the Expectectaion of $g(x)$ for the condition that $x\geq Q$, i.e. $\mathbb{E}[g(x)\ | \ x\geq Q]$.
$$g(x) = \frac{A}{\exp(-bQ+c)}\Big(\frac{1 + \exp(-bQ+c)}{1 +...
Mary Boas attempts to explain this by pointing out that the situation cannot arise because charges will have to be placed individually, and in an order, and that order would represent the order we sum in. That at any point the unplaced infinite charges would form an infinite divergent series...
My probability class has me wondering about pure math questions now. We started with the axioms and are slowly building up the theory. Everything was fine but then a definition of Conditional Probability P[A|B] = \frac{P[AB]}{P} appeared and it's just not sitting right with me. I know that...
Can someone help me on this question? I'm finding a very strange probability distribution.
Question: Suppose that x_1 and x_2 are independent with x_1 ~ geometric(p) and x_2 ~ geometric (1-p). That's x_1 has geometric distribution with parameter p and x_2 has geometric distribution with...
Confused and not sure if it is correct, but please do correct my steps.
We let event B be that there are at least 3 customers entering in 5 minutes.
Hence P(B) = 1- P(X=0)- P(X=1) - P(X=2) = ##1- \dfrac{e^{-5}5^{0}}{0!}-\dfrac{e^{-5}5^{1}}{1!}-\dfrac{e^{-5}5^{2}}{2!} ## = 0.8753...
Now we let...
Summary:: There's 11 fruits, 3 of which is poisionous.
A guy eats 4 of them, a girl eats 6 and a dog gets the last one.
What is the conditional probability of both the girl and guy dying IF the dog made it? One fruit is enough to kill you.
$$P(dog lives) = 8/11$$
$$P(allPeopleDie | dog...
We have a sample of X, a Normalized Gaussian random variable.We divide the data into positive and negative.
Each will have a conditional variance of ## 1−\frac{2}{π}## .
Can someone show how to get this result ?
I found this problem here (page 3) ...
Sir/madam,
I request you to solve 2 questions ( q-3 and q-5 ) of symbolic logic ( Strenthened method of conditional proof ).
These questions are taken from I.M.Copi's 'symbolic logic' ( edition -5, sec. 3.8, pg- 61 )
File is being attached.
thank you
yours truly
Deep Kumar Trivedi
1. Definition
If E and F are two events associated with the same sample space of a random experment, the conditional probability of the event E given that F has occurred, i.e. P(E|F) is given by
P(E|F) = (E∩F)/P(F) (P≠0)
2. Properties of conditional probability
Let E and F be events of...
I know that ##P(A,B) = P(A|B) \ P(B)##. But If i should like to define conditional probabilities for already-conditioned probabilities ie.
$$P(A,B|C)$$
how should I do it?
Writing something like ##P(A,B|C) = P(A|B|C) \ P(B|C)## seems nonsensical, and I've seen stuff that suggests ##P(A,B|C) =...
I am a noob to this topic so correct me If I made any silly mistake. By plugging in the values I managed to get
p(abc)=0.75*0.9*p(c|ab)
Here How can I find p(c|ab)? Is this question unsolvable or can I derive it?
I also want to know what is meant by p(abc) in literary terms.
I also created a...
I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition).
I am focused on Chapter 2: Sequences and Series of Real Numbers ... ...
I need help with the proof of Proposition 2.3.22 ...
Proposition 2.3.12 reads as follows:
Can someone please demonstrate (formally and...
Question: "In a lottery game each player tries to guess right 6 numbers designated in advance by choosing randomly from among numbers from 1 to 20. Given that one player guessed right 5 numbers out of 6 that he/she picked, what is the probability of guessing right the 6 numbers?"
The problem...
##P(T=1|W=w)=\frac{P(\{T=1\}\cap\{W=w\})}{P(W=w)}=\frac{\binom {n-2} {w-1} p^{w-1}(1-p)^{(n-2)-(w-1)}}{\binom n w p^w (1-p)^{n-w}}=\frac{(n-2)!}{(w-1)!(n-w-1)!}\frac{w!(n-w)!}{n!}\frac{1}{p(1-p)}=\frac{w(n-w)}{n(n-1)}(p(1-p))^{-1}##.
I cannot seem to get the terms with ##p## out of my expression.
There are 4 books being sold in the bookshop : A, B, C, D.
We know that 20% of the male customers buy book A at least once a week, 55% buy book B at least once a week, 25% buy book C at least once a week and 15% buy book D at least once in a month.
We also know that 32% of the female customers...
For 1) I found two ways but I get difference results.
The first way is I use P(A|B) = P(A and B)/P(B).
I get P(X<1|Y<1)=(∫_0^1▒∫_0^1▒〖3/4 (2-x-y)dydx〗)/(∫_0^1▒∫_0^1▒〖3/4 (2-x-y)dydx〗+∫_1^2▒∫_0^(2-x)▒〖3/4 (2-x-y)dydx〗)=6/7
The 2nd method is I use is
f(x│y)=f(x,y)/(f_X (x)...
Greg Bernhardt submitted a new blog post
AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic Conclusion
Continue reading the Original Blog Post.
Greg Bernhardt submitted a new blog post
AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic
Continue reading the Original Blog Post.
Homework Statement
Suppose that the number of eggs laid by a certain insect has a Poisson distribution with mean ##\lambda##. The probability that anyone egg hatches is ##p##. Assume that the eggs hatch independently of one another. Find the expected value of ##Y##, the total number of eggs...
Hello.
I am reading an online stats book, and there is the following question, which I solved incorrectly, and I think I understand what is my mistake, but I will be grateful for your explanation, if I have incorrectly detected the logic behind my mistake. I am weak at math (trying to improve it...
I am having a hard time with the following exercise:
Assume for this problem that the company has 8 Chevrolets and 4 Jeeps, and two cars are selected randomly and given to sales representatives.
What is the probability of both cars being Chevrolets, given that both are of the same make?
I...
Hey! I need help with my Math homework :( The question is the following...
There are 5 history courses of interest to Howard, including 3 in the afternoon, and there are 6 psychology courses, including 4 in the afternoon. Howard picks a course by selecting a dept at random, then selecting a...
Homework Statement
Out of all the products a company makes 2% is damaged. During the routine control of the products, the products are put to a test which discovers the damaged ones in 99% of the cases. In 1% however it approves the damaged item as a working one and vice versa. Find the...
Homework Statement
what is the probability that a component which is still working after 800 hrs, will last for at least 900hrs
Homework Equations
conditional probability
P(E|A) = ( P( E ∩ A) ) / ( P(A) )
The Attempt at a SolutionIm just checking my own understanding if this problem is...
I am working on Value at Risk and expected shortfall/conditional Value at Risk.The formula I have is this:
What I do not understand is numerator of the second part. If for example I want to look at an expected shortfall when p=0.01 (ignoring the average and the standard deviation). what value...
I'm currently stuck on a question that involves conditional probability with 3 events. This is a concept that I'm having the most trouble grasping and trying to solve in this subject. I am not sure how to start this problem.
The Question:
Given that P(A n B) = 0.4, P(A n C) = 0.2, P(B|A)=0.6...
Hi
In Dudas Pattern Classification, he Writes that P(x,\theta|D) can always be written as P(x|\theta,D)P(\theta|D) . However, I cannot find any justification for this. So, why are these Equal?