Conditional Definition and 447 Threads

What I mean by this is, Say I roll a die, given the specific condition that I get four eights consecutively such as "8888", the same probability as if I give the specific condition that I get another specific non-consecutive number such as? "0248" Thanks

1. Given f(x,y) = 2, 0<x<y<1, show V(Y) = E(V(Y|X)) + V(E(Y|x)) Homework Equations I've found V(Y|X) = \frac{(1-x)^2}{12} and E(Y|X) = \frac{x+1}{2} The Attempt at a Solution So, E(V(Y|X))=E(\frac{(1-x)^2}{12}) = \int_0^y \frac{(1-x)^2}{12}f(x)dx, correct?

Bob picks 3 cats. There are 5 striped males, 6 striped females, 8 spotted males, and 4 spotted females. What is the prob. that Bob has atleast a striped cat given that he has picked at least a female? ------------------------------------------------------ I have: (prob. of a striped...

A conditional statement is of the form A→B. Truth tables suggest that the converse, B→A ≠ A→B. It is also known that any two vectors A and B are perpendicular if and only if their dot products are zero. My confusion is... A dot B = 0 → A and B are perpendicular. The converse is...

1. You give a friend a letter to mail. He forgets to mail it with probability 0.2. Given that he mails it, the Post Office delivers it with probability 0.9. Given that the letter was not delivered, what’s the probability that it was not mailed? 2. I assume I'm supposed to use Bayes...

Hi there, I have the journey times of 2 journeys. Would somebody be able to show me by way of example how to calculate the conditional probability function of the second journey time given the first journey time? https://dl.dropbox.com/u/54057365/All/jt.JPG Appreciate your help Thanks John

1. Let the joint pdf be f(x,y) = 2 ; 0<x<y<1 ; 0<y<1 Find E(Y|x) and E(X|y)Homework Equations E(Y|x) = \int Y*f(y|x)dy f(y|x) = f(x,y) / f(x) The Attempt at a Solution f(x) = \int 2dy from 0 to y = 2y f(y|x) = f(x,y)/f(x) = 1/2y E(Y|x) = \int Y/2Y dy from x to 1 = \int 1/2 dy from x to 1 =...

Hi all, I need help regarding the following expression: E(x1|X>K) where: x1 is a one dimension normal rv X is multivariate normal rv with n components: x1, x2,..., x_n K is a n dimension constant vector with n components: k1,k2,...,k_n X>K <==> x1>k1,x2>k2,...,x_n>k_n I know there is...

Homework Statement Of the items produced daily by a factory, 40% come from line I and 60% from line II. Line I has a defect rate of 8%, whereas line II has a defect rate of 10%. If an item is chosen at random from the day’s production, find the probability that it will not be defective...

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[B]} appeared and it's just not sitting right with me. I know that...

P(S1 \cap S2 \cap S3 | r) How do I simplfy the above equation if S2 and S3 are independent of r ?

I have some problems getting conditional probability right... Does this look like it should? Homework Statement Assume that there are bags of tulip bulbs in the basement, ant that they contain 25 bulbs each. yellow bags contain 20 yellow tulips and 5 red tuplips, and red bags contain 15 red...

Hi guys, assume we have an equality involving 2 random variables U and X such that E(U|X) = E(U)=0, now I was told that this assumption implies that E(U^2|X) = E(U^2). However I'm not sure on how to prove this, if anyone could show me that'd be great!

NOT talking about nonabsolute vs absolute convergence. I'm talking about conditional convergence. In my analysis text, this was a bit that was covered as enrichment and it straight up blew my mind. I don't get it. How can you simply rearrange terms and come up with a separate sum? They showed a...

1. I am going over some past Probability exam papers and cannot solve this question. Any help or advice would be much appreciated! 2. David eats cereal for lunch 60% of days. If he had ice cream for breakfast, then the probability that he eats cereal for lunch is only 0.25. If he didn't...

I am working on studying for a probability exam and I just came across conditional variance, but I can't find anything in my materials for how to solve it. If I want to find the conditional variance of Y given that X=x, or Var[Y|X=x], how would I solve it? I am given a continuous distribution...

I am working on studying for a probability exam and I just came across conditional variance, but I can't find anything in my materials for how to solve it. If I want to find the conditional variance of Y given that X=x, or Var[Y|X=x], how would I solve it? I am given a continuous distribution...

Homework Statement Suppose you have 3 nickels and 4 dimes in your right pocket and 2 nickels and a quarter in your left pocket. You pick a pocket at random and from it select a coin at random. If it is a nickel, what is the probability that it came from your right pocket? 2. The attempt at a...

You are given a random exponential variable X: f(x) = λ exp(-λ x). Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X: Y = IP(X), Z = FP(X). Which is the following conditional probability: P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?

Hello, I'm trying to work out a conditional probability. I have hundreds of measurements of two variables (1) Start Time and (2) Journey time. I've created a frequency table. https://dl.dropbox.com/u/54057365/All/forum.JPG How can I work out the Journey time given a start...

Hello, I'm trying to work out a conditional probability. I have hundreds of measurements of two variables (1) Start Time and (2) Journey time. I've created a frequency table. https://dl.dropbox.com/u/54057365/All/forum.JPG How can I work out the Journey time given a start time? P(JT |...

Hi, all. I happened to think about a problem about conditional PDF: x_2=x_1+a, x_1 \approx \mathcal{N}(0,1), a \approx \mathcal{N}(0,1) so the conditional PDF of f(x_2|x_1), f(x_1|x_2) would both be f(x_2|x_1)=f(x_1|x_2)=\frac{1}{\sqrt{2\pi}}\exp{(-\frac{(x_1-x_2)^2}{2})} And it is clear...

Homework Statement The Attempt at a Solution I have that the joint probability mass function would be \Pi_{i=1}^{k} \frac{\lambda_{i}^{n_{i}}}{n_{i}!} e^{-\lambda_{i}} How would I go about applying the conditional to get the conditional distribution?

Hi all, My question is the following. Let's say I have two probability distributions; f(x|b)\,g(x|c) b and c are discrete events while x is a continuos variable. i.e When the button b is pressed there is some distribution for the amount of rain fall the next day, x. When the button c...

Need help A system contains two components A & B. The system will function so long as either A or B functions. The probability that A functions is 0.95, the probability that B functions is 0.90, & the probability both function is 0.88. What is the probability that the system functions.

f[x_] := x^2 + c; y = Solve[f'[f[x]] == 1, x, Reals] output: {{x -> ConditionalExpression[Root[-1 + 4 c #1 + 4 #1^3 &, 1], c > -(3/4) || c < -(3/4)]}, {x -> ConditionalExpression[Root[-1 + 4 c #1 + 4 #1^3 &, 2], c < -(3/4)]}, {x -> ConditionalExpression[Root[-1 + 4 c...

T ≡ "two coins tossed 7 times by two people A and B giving outcomes [A^+B^+, A^-B^+, A^+B^-, A^-B^+, A^+B^+, A^-B^-, A^-B^+], where + = heads and - = tails" Calculate P(A^+B^+|T), P(A^+|T), P(B^+|T) and P(B^+|T,A^+) I asked this question elsewhere and there was a suggestion that the question...

Homework Statement The Attempt at a Solution a) P(Pickwick has no umbrella | it rains) = \frac{\frac{1}{3}\frac{1}{3}}{\frac{1}{2}} = \frac{2}{9}, which is the answer according to my answer key. b) For part b we have: There is a rain forecast which means he will bring the...

Homework Statement Compute P(X=k l X+Y=p)Homework Equations The Attempt at a Solution No idea. Kind of understand page #1. Although it seems like there's a lot of unnecessary stuff. Could have gone straight from the top to the bottom. And I don't know why/if you even have to substitute the...

My professor explained this concept absolutely horribly and I have no idea how to do these problems. Let A and B be independent Poisson random variables with parameters α and β, respectively. Find the conditional expectation of A given A + B = c. (Hint: For discrete random variables, there...

At the bottom of the page (example 2) for question c) P(B|A'). They say P(B n A') = 0.2. But surely it is (B while not A) which in my mind should be 0.15. Can somebody tell why it is 0.2?

Homework Statement I've spent a few hours but unable to work out the solution of the following questions successfully. The question is as follows: I am having problems with (a)(iii) and (b)(ii) Homework Equations The Attempt at a Solution (a)(iii) Although I can work...

Guys my question should be easy but I cannot understand how it works, here is how it goes. A murder case involves the death of a guest at a large party in a country house. The police are certain that there is only one murderer who is among the N = 100 remaining people in the house. However...

Homework Statement An image of the assigned problem is here: http://imgur.com/aYkaM Homework Equations The formula for being exponential, gamma, and probably Bayes's Law. They'd take a while to type out, and presumably anyone who can help me with this already knows the formulas or...

Hi guys, I can't get my head around this, if anyone could help that would be great. "A robotic assembly line contains 20 stations. Suppose that the probability that each individual station will fail is 0.3 and that the stations fail indepen- dently of each other. Given that at least one...

I've been looking at the measure theoretic definition of a conditional expectation and it doesn't make too much sense to me. Consider the definition given here: https://en.wikipedia.org/wiki/Conditional_expectation#Formal_definition It says for a probability space (\Omega,\mathcal{A},P), and...

I have seen in class the following formula used: P(A | C) = \sum_{B} P(A | B \cap C)*P(B | C) I don't understand how this formula works? Can anyone help me understand how it can be derived and how I can understand it intuitively? Can a venn diagram be drawn to illustrate this formula?

Homework Statement I have access to P(x|A) and P(y|A), P(x), P(y) and P(A), in addition to the knowledge that x and y are independent variables. I am interested in finding P(A|x,y). The Attempt at a Solution I think that P(A|x,y) = P(x,y|A) * P(A) / P(x,y) = P(x,y|A) * P(A) /...

Homework Statement A submarine has three navigational devices but can remain at sea if at least two are working. Suppose that the failure times are exponential with means 1 year, 1.5 years, and 3 years. What is the average length of time the boat can remain at sea?Homework Equations Density...

Homework Statement So what I was taught was that if the lim of the ratio test is the series is always absolutely convergent. If it is >1 the series is always divergent. But if it is =1 then we don't know. So would that mean that all conditionally convergent series would have a limit = 1? I...

So If B=B1UB2U...UBn would Pr(A|B)=Pr(A|B1)Pr(B1)+Pr(A|B2)Pr(B2)+...+Pr(A|Bn)Pr(Bn)? I haven't found a formula for this but it makes intuitive sense.

Conditional probability & "r balls randomly distributed in n cells" Homework Statement I'm posting this in hope that someone can give me a correct interpretation of the following problem (problem V.8 of Feller's Introduction to probability theory and its applications VOL I): 8. Seven balls...

Homework Statement A box contains 4 red balls and 6 white balls. A sample size of 3 is drawn without replacement from the box. What is the probability of obtaining 1 red ball and 2 white balls given that at least 2 of the balls in the sample are white? Homework Equations The...

Homework Statement This is a problem I found on web but with no solutions. n Exercise 11 from "Problems on Minterm Analysis," we have the following data: A survey of a represenative group of students yields the following information: 52 percent are male 85 percent live on campus 78...

Say I want to find Pr(A|B). Usually I would just use bayes rule, but some textbooks just assume that A|B works and then just multiply it by P(B). For example in my book, Pr(X>2000)=.4. X and Y are unif distributed from 1000 to 5000. They are independent. Find Pr(X+Y>8000|X>2000). Well they just...

Homework Statement This is in fact an example with solutions. but I don't understand the solutions. So I am here to ask for explanation. Details are; In a city there are equal number of gentleman and ladies. 10% of gentleman are regarded as "good-looking" while 10% of ladies regarded as...

Homework Statement 45% of emails sent to my account is spam. i set up a filter but it fails toquarantine 2% of spam and in advertently quarantines5% of genuine emails. What is the probability that an email will be quarantined as spam? if an email is qurantined as spam what is the...

Homework Statement \sum from n=1 to n=\infty (1 + \frac{x}{n})n2 Determine the values of x for which the series converges absolutely, converges conditionally and diverges.The Attempt at a Solution So i tried using the root test for the absolute value of (1 + \frac{x}{n})n2, but it was...

Homework Statement Let Ω = [0,1] with the σ-field of Borel sets and let P be the Lebesgue measure on [0,1]. Find E(X|Y) if: Homework Equations X(w)=5w^2 Y(w)= \left\{ \begin{array}{ll} 4 & \mbox{if $w \in [0,\frac{1}{4}]$} \\ 2 & \mbox{if $w \in (\frac{1}{4},1]$} \\ \end{array}...

I know this isn't quite advanced probability, but I'm not sure if I have this right. I want to show that conditional independence of $X$ and $Y$ given $Z$ does not imply independence of $X$ and $Y$ (and vice versa). So I used coin tosses where: $X=\{$ first coin tails $\}$ $Y=\{$ second coin...