Conditional Definition and 447 Threads

So we learned about the basic tests for convergence of an infinite series, and we learned about alternating series, and conditional convergence. Now, I get how to find if a series is conditionally convergent. But what's the use of conditionally convergent infinite series? All we were taught...

The difference btwn marginal distribution and conditional distribution ? So I have a table that "apparently" shows how a company's employees commute to work. TRANSPORTATION JOB CLASS CAR BUS TRAIN TOTAL...

In an election, candidate A receives n votes and candidate B receives m votes, where n>m. Assume that in the count of the votes all possible orderings of the n+m votes are equally likely. Let Pn,m denote the probability that from the first vote on A is always in the lead. Find Pn,m...

[Problem] Stores A, B, and C have 50, 75, and 100 employees, respectively, 50, 60, and 70 percent of these are women. Resignations are equally likely among all employees, regardless of sex. One employee resigns and this is a woman. What is the prob. she works in store C? [Solution] Store A...

Let X, Y be independent exponential random variables with means 1 and 2 respectively. Let Z = 1, if X < Y Z = 0, otherwise Find E(X|Z) and V(X|Z). We should first find E(X|Z=z) E(X|Z=z) = integral (from 0 to inf) of xf(x|z). However, how do we find f(x|z) ?

Let {Nt, t>0} be a Poisson process with arrival rate \lambda. Consider a process {Xt = exp(Nt-a*t, t>0}. How to calculate E[Xt|Xs] for 0<s<t.

[SOLVED] Conditional Expectation I'm trying to understand the following proof I saw in a book. It says that: E[Xg(Y)|Y] = g(Y)E[X|Y] where X and Y are discrete random variables and g(Y) is a function of the random variable Y. Now they give the following proof: E[Xg(Y)|Y] = \sum_{x}x g(Y)...

conditional probability help please Homework Statement Hi there, I am doing s1 for this jan and i am finding it very difficult to cope up. Especially for probability. I have a cgp buk but stil its not very gud at probability. Here is a question from my text buk which i cud not understand : -...

i need to covert the following conditional statements into logical notation using propositional connectives and quantifiers: a) A has at most one element b)A is a singleton c)ø ∈ A you don't have to give me the answers, just help me get started or give me some hints

I'm having trouble seeing how this works out. It's blatantly obvious that this is true, but somehow I can't seem to get anywhere on paper with it to simplify it down to anything. Any help would be greatly appreciated! P\left(A\right|B)=1-P\left(not A\right|B)

Homework Statement The probability of a monitor not working is 0.005, the probability of a cpu faulty is 0.002, the probability of a keyboard damaged is 0.0025, what is the probability of the computer switching on? If you are then told that the conditional probability of the monitor not...

I am trying to practice for an exam but can't do this question: does the series \((-1)^n/ln(n) from n = 2 to infinity converge abs/conditionally/diverge? I know if a do an alternating series test, the integral will converge because lim goes to 0 and a(n+1)<an. But how can I prove that...

Hi all First of all, I am new here but I am not new to statistics. But I need your help:smile: I do have a multivariate normal distribution: x~p(mu,sig) the vector x has to groups of variables, those that I know are below zero (x_bz), and those that I know are above zero (x_az). I am...

Homework Statement Assuming a comp is switched on, the probability that the monitor is not working is 0.005, the probability that the CPU is faulty is 0.02, and the probability that the keyboard cable has been damaged is 0.0025, and that there are no other faults. Proceed to evaluate the...

I say urgent because of the horribly small lecture I received on this section, a whole 3 minutes or so of examples. While I won't give further context I can say without a doubt I am completely lost. Here is the problem I am stuck on. In a string of 12 Christmas tree light bulbs, 3 are...

Homework Statement Show that \left[\neg\,p\,\wedge\,\left(p\,\vee\,q\right)\right]\,\longrightarrow\,q is a tautology without using truth tables. Homework Equations DeMorgan's Laws, etc. The Attempt at a Solution...

Hi, Let x,z continuous random vectors and n discrete random vector: n=[n1,n2,...]. I'm trying to find for instance, E_z|n3{ E_n|z(x)} = ?. Thanks...

I've been staring at this for hours. Any hints? Let the vector Y = (Y_1,Y_2,\dots,Y_k) have a multinomial distribution with parameters n and \pi = (\pi_1,\pi_2,\dots,\pi_k): \sum_{i=1}^{k}Y_i = n, \quad \sum_{i=1}^{k}\pi_i = 1 Show that the conditional distribution of Y_1 given...

I need to get the density function of a Beta distribution (call it B) with it's two parameters, X and Y, binomially distributed. 1) My first question is, would I be right in saying that the density function that I am looking for can be defined as a "conditional Beta distribution". ie...

hi I got a stats problem infornt of me. I figured out that it is abaut conditional probability. But I am stuck :confused: . # hurricanes 0 1 2 3 4 5 6 probability .25 .33 .24 .11 .04 .02 .01 prob >6 is 0 questions are independent. a.)...

At school we have begun conditional probability. Of course, using the conditional probability formula to answer questions is no problem; but i do not fully understand how the formula works. The formula is; Pr(A given or │ B)= Pr(A intersection B)/Pr(B) The the proof for it is self evident...

Quantum Mechanics assigns a probability of measuring a final state given an initial state. This suggests a conditional probability of obtaining |final> on the condition that you first have |initial>. But since the probability of |s> obtained from the same initial state |s> is 1, in other words...

Hi Everyone, Let's see if someone here can do a better job than my teacher! I have one of the least helpful stat teachers ever. She told me that I was wrong about the following problem. I am not saying that she is wrong or right, but when I asked her to explain why I was wrong, she told me...

Given: P(A)= .4, P(B)=.3, P(A n B)=.11, P(C| not A)=.5 If P(C U A) = .66, then find P[(C U A) | (C n A)]. I have been trying to manipulate this thing for a while now with no luck. Could you try and show the work if not that's alright, I'll work it out. Thanks.

Question: Deer ticks can carry both Lyme disease and human granulocytic ehrilichiosis (HGE). IN a study of ticks in the Midwest, it was found that 16% carried Lyme disease, 10% had HGE, and that 10% of the ticks that had either Lyme disease or HGE carried both diseases. (a) What is the...

I have to admit I'm struck odd by the this definition: P(A|B) = P(AnB)/P(B) I know conditional probability is the "chance of event a dependant even B happening, given A happens". But really, I don't quite get it... what is meant?

I'm having a problem evaluating a distribution- Suppose X and Y are Chi-square random variables, and a is some constant greater than 0. X and Y are independent, but not identically distributed (they have different DOFs). I want to find P(X>a,X-Y>0). So I use Bayes' theorem to write...

I need help in solving the following problem: Let X be uniformly distributed over [0,1]. And for some c in (0,1), define Y = 1 if X>= c and Y = 0 if X < c. Find E[X|Y]. My main problem is that I am having difficulty solving for f(X|Y) since X is continuous (uniform continuous over [0,1])...

Any hints on how to solve for E(Y|X) given the ff: Suppose U and V are independent with exponential distributions f(t) = \lambda \exp^{-\lambda t}, \mbox{ for } t\geq 0 Where X = U + V and Y = UV. I am having difficulty finding f(Y|X)... Also, solving for f(X,Y), I am also having difficulty...

Is it possible to solve for E(Y) and var (Y) when I am only given the distribution f(Y|X)? I can solve for E(Y|X). But is it possible to find E(Y) and var(Y) given only this info?

if X and Y are events which are independent of each other, but neither are independent with A, is this equality true for conditional probabilities: P( X, Y | A) = P(X|A) * P(Y|A) if not, how do you solve for P(A | X,Y) given that you only know P (A) and P(X|A) and P(Y|A)? The reason I came...

Please help me to solve the following questions : 1) There are three box : box X has 10 bulbs which 4 are defective Box Y has 6 bulbs which 1 are defective Box Z has 8 bulbs which 3 are defective a box is chosen at random...

An insurance company runs three offices, A, B and C. The company's employess are distirbuted as follows; 30% work in office A, 20% in Off. B and 50% in Off. C. In office A 10% are managers, in office B 20% are managers and in office C 5% are managers a. What is the total proportion of...

Q. A box contains three blue marbles, five red marbles, and four white marbles. If one marble is drawn at random, find: a) P(blue|not white) b) P(not red|not white) The answer for both a) and b) is 3/8. However right now I don't even understand the question. part a) wants possibility of...

Hi, We're debating the question "Can a series of nonnegative numbers converge conditionally?" I say no becuase if all of the terms are nonnegative then they are the same as their absolute values. My classmate disagrees and says that there is a series that has nonegative terms whose absolute...

Hey guys Me and my friend just got this question and it seems easy but i just want to make sure we are right anyway here it is: A road has two stoplights at consecutive intersections. The prob. of a red at the first is 0.55 and the probability of a green at the second, give a green at light...

the discrete prob distribution X/Y - G - D 0 - 0,1 - 0,15 1 - 0,1 - 0,3 2 - 0,05 - 0,3 this is what i have so far: E[X|Y=D]=0,2 E[X|Y=g]=0,9 E[X]=0,725 E[X^2|Y=D]=0,3 E[X^2|Y=G]=1,5 Var(X|Y=G)=0,69 Var(X|Y=D)=0,26 i.e. [X]=0,2*0,25 + 0,9*0,75=0,725 is the previous...

Prove this questions using ration ideal in intuitive way. Prove this implications and explain the results: (a) A _|_ B => not A _|_ not B, onde _|_ means that events A and B are independent. (b)[ P(A|C) >= P(B|C) ] and [ P(A|not C) >= P(B|not C) ] ==> P(A) > P(B)

Question about conditional probability. Can someone help me ? Repulsion. The event A is said to be repelled by the event B is P(A|B) < P(A), and to be attracted by B P(A|B) > P(A). (a) Show that if B attracts A, then A attracts B, and ~B repels A. (b) If A attracts B, and B attarcts C...

Can someone help me with this question ? A random number N of dice is thrown. Let Ai be the event that N = i, and assume that P(Ai) = 1/(2)^i, i >= 1. The sum of the scores is S. Find the probability that: (a) S = 4, given N is even; (b) the largest number shown by any die is r, where S...

hello all I have been workin on some problems involving conditional probability and continuous random variables and the thing is i don't know if i get the limits correct, anyway here is the problem, check it out, any suggestions would be helpful f(y_1,y_2)...

conditional density function - need help please! given a signal x, is a random variable which is expontential with a mean of 3. it is transmitted through an additive gaussian noise channel, where the gaussian noise has a mean of -2 and a variance of 3. the signal and noise are...

Ok guys, I don't really understand conditional probability, can you guys tell me how to go about solving this? To please customers, repairs need to be done satisfactorily and completed on time. For one mechanic, if the job is done on time, he has a 85% chance that it was also done...

I missed my data management class on friday and now If find out I have a quiz tomorrow on the stuff I missed. I got fridays sheet but these questions seem really dumb and kind of confusing. Some of them seem so simple they are confusing. here are some of the ones that confused me that maybe you...

so P(A|B) = P(A intersect B)/ P(B). so, P(A intersect B) is the same as P(A) * P(B) right? so doesn't the P(B) always cancel out, and the answer will always be P(A)? That doesn't makes sense at all... :confused: for example: A family has 2 children, and all possibilites are equally...

I just need a guide to this problem... found in one of the books in the library... Given the joint pdf f(x,y) = 2e^[-(x+y)] where 0 < x < y, y > 0 find P(Y < 1 / x < 1). Note that "/" means given that. I got the formula when P(a < Y < b / X = x) is given, i.e., in terms of the integral...

In a class of 15 students, 10 are expected to pass maths and 12 are expected to pass english. how many students are expected to pass maths and english? ----- the answer given in the book is 7. i don't understand how this answer was reached. could someone please show me how to calculate...