Conditional Definition and 483 Threads

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...

I wanted to compute the conditional pearson correlation (CPC). First, I wanted to make sure if it is OK to use the absolute pearson correlations in the computation of CPC. Becuase I think only the strength of pairwise correlations should be considered in computing CPC, and not the sign. Second...

Homework Statement Suppose that X and Y have a continuous joint distribution with joint pdf given by f (x, y) = { x + y for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 0 otherwise. Suppose that a person can pay a cost c for the opportunity of observing the value of X before...

Hi everyone. I have never worked in-depth with Excel and I am trying to make my life a bit simpler doing some data cleaning using the 'conditional formatting' option. My scenario is the following: I have two columns of data, column A and column B. I would like to take each entry (a string...

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...

I was able to do the first part of this problem but unsure how to approach this: Mendel, revisited: Mendel’s peas had either purple or white flowers; flower color is due to a single gene, for which the purple allele (A) is dominant to the white allele (a). We cross two pure-breeding lines...

Homework Statement All athletes at the Olympic games are tested for performance-enhancing steroid drug use. The imperfect test gives positive results (indicating drug use) for 90% of all steroid-users but also (and incorrectly) for 2% of those who do not use steroids. Suppose that 5% of all...

Homework Statement A manufacturer of scientific workstations produces its new model at sites A, B, and C; 20% at A, 35% at B, and the remaining 45% at C. The probability of shipping a defective model is 0.01 if shipped from site A, 0.06 if from site B, and 0.03 if from site C. A- What is...

Homework Statement Two computers are connected to a password-protected wireless network. When the password is temporarily removed, a virus can attack the first computer with probability 0.5, the second computer with probability 0.7, and it can attack both computers with probability 0.4. The...

Homework Statement I've attached both the problems into one image to make life easier since problem 1 has a diagram and the other does not. Homework Equations Bayes Theorem : P(A|B)P(B) / [P(A|B)P(B) + P(A|B')P(B')] B' = B Complement The Attempt at a Solution well for the first one i don't...

Hello, I am stuck with the following question. 1. Suppose T ind. C |Z, does it follow that T ind. C ? 2. Suppose T ind. C , does it follow that T ind. C |Z? I think both don't follow, but I don't know how to show it Thanks in advance

Homework Statement You have 3 urns: Urn 1 has 3 red balls, Urn 2 has 2 red balls, 1 blue ball. Urn 3 has 2 red balls 2 blue balls. You pick a ball from each urn and place it into Urn 4. You draw 2 balls from Urn 4 and they are red. What is the conditional probability that the 3rd ball is also...

A number is selected randomly from a container containing all the integers from 10 to 50 find a) p(even|greater than 40) b) p(greater than 40| even) c) p(prime| between 20 and 40) please provide an explanation, thanks a lot =D

Please, help me to solve the problem Details at a factory are tested randomly to check if they are faulty. It is known from previous experience that the probability of a faulty detail is known to be 0.03. If a faulty detail is tested the probability of it testing faulty is 0.82. If a non-faulty...

Hey guys, first of all I want to say hey to all! I have been a long time lurker and follower of these forums and have been known to find a lot of your answers helping me out throughout my college life. I also know that you just don't like to spit out the answers for those who don't put in...

Two coins are flipped and the results are recorded. Given that one coin lands on a head, find the probability of: a) Two heads, b) a head and a tail Searching online is giving my answers which are not using conditional probability at all, and our teacher told us we have to use the...

I was reading this article of wikipedia: Conditional and absolute convergence It says: "An absolutely convergent sequence is one in which the length of the line created by joining together all of the increments to the partial sum is finitely long." Is that a characterization of...

Product Testing A supposed coffee connoisseur claims she can distinguish between a cup of instant coffee and a cup of drip coffee 75% of the time. You give her 5 cups of coffee and tell her that you will grant her claim if she correctly identifies at least 4 of the 5 cups. (a) What are her...

1. Homework Statement ******* SOLVED ********* There are three magazines A,B and C respectively. A survey of readers was taken and the following data was collected. 0.6 Read A 0.5 Read B 0.5 Read C 0.3 Read A&B 0.2 Read B&C 0.3 Read A&C 0.1 Read A&B&C What is the probability that a reader...

I have a question about the ratio test. Suppose it proves inconclusive, we must than use another test to check for conditional convergence - 1) this test has to be associated with an alternating series, such as the Alternating Series Test, correct? (we wouldn't be able to use something like...

The random variable X has the PDF fX(x) = cx^-2 if 1 < x < 2; 0 otherwise: (a) Determine the value c (b) Let A be the event fX > 1.5. Calculate the conditional expectation and the conditional variance of X given A. I'm not understanding the concept of conditional pdf's. Can someone show me the...

Homework Statement I have two kids. Given that at least one of them is a girl, what is the probability that they are both girls? Homework Equations The Attempt at a Solution I think it's 1/3, because the possibilities are: Boy Boy, Boy Girl, Girl Boy, Girl Girl. There are three...

Hello, I'm somewhat confused by the expression f(X = x | Y = y) = \frac{f(X=x)}{f(Y=y)} (which, if I'm right, is the definition of a conditional probability density? My course seems to state it as a theorem, without proof, but then again my course is a little bit vague; although I welcome...

My book tries to illustrate the conditional expectation for a random variable X(\omega) on a probability space (\Omega,\mathscr F,P) by asking me to consider the sigma-algebra \mathscr G = \{ \emptyset, \Omega \}, \mathscr G \subset \mathscr F. It then argues that E[X|\mathscr G] = E[X] (I'm...

Hello, I want to compute the conditional entropy H(A | B,C), given probability distributions for each of the variables. It would be nice to have a right-hand side not involving conditionals. H(A|B) = H(A,B) - H(B) but how does it work out if there are more than one conditional variable...

1) I'm trying to prove that two R.V.s X & Y are related iff Y & X are related. Assuming they are discretely distributed. So basically from what I've learned is that two R.V.s are related if the joint pdf changes as Y changes. So basically if f(X|Y=yi) changes when i changes. So from that...

need urgent help with a conditional variance proof. I have been given this problem and I'm pretty stumped. I want to prove that Y=g(X) if and only if var(YlX) = 0. so if var(YlX)=0 then E(Y^2lX) - E(YlX)^2 = 0 E(Y^2lX) =E(YlX)^2 so what should I do now? I tried showing that this...

I have a simple-seeming question on conditional expectation. It seems simple, but it has eluded my attempt to answer. Suppose that two jointly distributed random variables (X,Y) exist with support on positive real line. From these, it is possible to construct a new random variable, Z=E[X|Y]...

Homework Statement Basically, I'm given the probability of 4 independent events: P(A) = 0.04 P(B) = 0.03 P(C) = 0.02 P(D) = 0.01 If anyone of these occur, a failure will happen. More than one can happen at the same time. I need to find the probability that more than one of them...

Homework Statement D = (L + E) / S Where L, E, and S are mutually independent random variables that are each normally distributed. I need to find (symbolically), the conditional PDF f(d|s). Homework Equations The Attempt at a Solution Not sure what to do with so many...

Homework Statement A bowl contains 10 chips: 6 red chips and 4 blue chips. three chips are drawn at random and without replacement. Compute the conditional probability that a) 2 are red and one is blue; given that at least 1 red chip is among the 3 selected b) all are red, given that at least...

Homework Statement You are a member of a class of 18 students. A bowl contains 18 chips: 1 blue and 17 red. Each student is to take 1 chip from the bowl without replacement. The student who draws the blue chip is guaranteed an A for the course. a)If you have the choice of drawing first...

Homework Statement An urn contains four colored balls: two orange and two blue. Two balls are selected at random without replacemen, and you are told that at least one of them is orange. What is the probability that the other ball it orange? Homework Equations Now, we have been...

Homework Statement romeo proposed to juliet. now he's waiting for her response. R = 'event that she replies' W='event that she wants to get married' Mon = 'event on monday' Tue = 'event on Tuesday' P(R\wedgeMon | W) = 0.2 P(R\wedgeTue | W) = 0.25 P(R\wedgeMon| \bar{W}) = 0.05...

Hi everyone, I have a feeling the following property is true but I can't find it stated in any textbook/online reference. Maybe it's not true... Can someone verify/disprove this equation? E(A+B|C) = E(A|C) + E(B|C)

Homework Statement I was wondering if anyone knows of a conditional statement that will prevent users from imputing non integer inputs. like for example z=0 while z<1 x=input('Enter Something') if SOME MAGICAL CONDITIONAL STATEMENT disp('You entered a invalid...