Conditional Definition and 447 Threads

Consider the conditional probability P(A|C) . Is it true that we can calculate above as Summation over B P(A|B)*P(B|C) .

Homework Statement (Question is #6 on p.171 in An Introduction to Probability and Statistics by Ruhatgi & Saleh) Let X have PMF Pλ{X=x} = λxe-λ/x!, x=0,1,2... and suppose that λ is a realization of a RV Λ with PDF f(λ)=e-λ, λ>0. Find E(e-Λ|X=1) The Attempt at a Solution The...

I could have posted this in the homework section but I didn't see a section on probability. Also, this is more of a general conditional probability question asked through an example. A band called Radiohead is inspired by an old band called The Beatles. 50% of music critics think the beatles was...

A band called Radiohead is inspired by an old band called The Beatles. 50% of music critics think the beatles was a great (G) band, 40% that it was moderate (M) and 10% that it was awful (A). These critics have also compiled the following table:0.8 0.1 0.1 0.1 0.9 0 0.2 0.3 0.5The table says...

What is the difference between switch statement and if statement?

Homework Statement 99% of all babies survive delivery. However, 10 % of all births involve Cesarean (C) sections, and when a C section is performed the baby survives 98% of the time. If a randomly chosen pregnant woman does not have a C section, what is the probability that her baby survives...

Homework Statement A card is picked at random from N cards labeled 1,2,...,N and the number that appears is X. A second card is picked at random from cards numbered 1,2,..., X and its number is Y. Find the conditional distribution of X given Y = y. Homework Equations P(X = x | Y = y) =...

Homework Statement 4 balls are placed successively into 4 cells, all 4^4 arrangements being equally probable. Given that the first 2 balls are in different cells (event B), what is the probability that one cell contains exactly 3 balls (event A)? Homework Equations P(A|B) = P(A...

In a paper, I have found this relationship: E(X|Y<y)=Cov(X,Y)*E(Y|Y<y)/Var(Y) It seems to me that the previous equation holds if, for instance, X=aY+Z with Z and Y independent and a non zero. It also holds if (X,Y) is a bivariate normal (with non zero correlation). But does it hold...

The attached equation is from http://en.wikipedia.org/wiki/Multivariate_normal_distribution can anyone show me why the conditional variance is equal to (1-rou^2)* variance of y thanks

So i a need to find E[XY], expected value of XY But the process of finding E[X] includes a long and tideous integral which i am trying to avoid. So computing E[XY] using its formula is also something i am trying to avoid. But could i use this identity? E[XY] = E[E(XY/Y)] = E[Y[E(X/Y)]]...

Hello, in relation to Markov chains, could you please clarify the following equations: In particular, could you please expand on why the first line is equal. Surely from , along with the first equation, this implies that: I just don't see why they are all equal. Please could you...

Homework Statement [PLAIN]http://img222.imageshack.us/img222/2781/statsqk.jpg Homework Equations f_{X} (x) = \int^{\infty}_{-\infty} f_{X,Y} (x,y)\;dy f_{Y} (y) = \int^{\infty}_{-\infty} f_{X,Y} (x,y)\;dx f_{X|Y} (x|y) = \frac{f_{X,Y} (x,y)}{f_Y (y)} f_{Y|X} (y|x) =...

Homework Statement Students who actively participate in class are 4 times more likely to get a good grade than those who don't. 15% of students actively participate in class; 20% of students get a good grade. A person did not participate in class, what is the probability that he got a good...

Homework Statement A radioactive source emits particles according to a Poisson process, at an average rate of λ per unit time. Each particle emitted has probability p of being detected by an instrument, independently of other particles. Let X be the number of particlese emitted in a given...

Hi everybody. I keep on reading Rohatgi's book "An introduction to Probability and Statistics" and I have worked out the following problem: "An urn contains r red marbles and g green marbles. A marble is drawn at random and its color noted. Then the marble drawn, together with c > 0 marbles of...

How do I find a conditional bionomial distribution? For example, if I want the probability that k=7 (for instance, 7 could be any number depending on the experiment), given that k is greater/equal to 4. I know what the equation would look like i.e.: F(k=7|k >= 4)= P(k=7, k>=4)/P(k>=4)...

Hi, This is a homework problem that I'm having a very hard time with. We are given that f(x)=e^(-x) for X greater/equal to zero. The question is to find f(x|A) where A is the union of the events (1 less/equal x, and x greater than 10). I can't figure out how to go about doing this...I...

Homework Statement I am familiar with the following kind of conditional expectation expression: \mathbb{E}[Y|X=x], where X and Y are random variables. I am wondering what the following conditional expectation stands for: \mathbb{E}[Y|X] How these two are related? How the second...

Homework Statement In a neighbourhood, 75% of households speak only English at home, and 5% speak only Spanish at home. Four households are randomly chosen. Given that at least one of the four households speaks only Spanish at home, what is the probability that only one speaks Spanish at...

Hello all, I'm reading through some code that someone else wrote and have come across the following conditional: if 0 figure; plot(times, average); end; I've never seen if used without a statement to test (ie: if x>0...) and I can't find any documentation on it anywhere...

Dear all, I am in need of an advice regarding a conditional probability... Although it is very simple, I haven't found anywhere anything similar so I am not sure I get it right...I tried numerically calculating this conditional probability using 2 approaches (in Mathematica) and I get 2...

The probability of surviving a certain operation is .55. If a patient survives the operations, the propability that his or her body will reject the transplant within a month is .20. What is the probability of surviving both these critical stages. I am going to say P(A) = .55 and P(B | A ) =...

Homework Statement Random variable U is continuous uniform in the time interval (0,2) T|U (T given U) is modeled by the mgf \frac{1}{1-ut} Find: a) E(U) b) E(T|U) and Var(T|U) c) E(T) and Var(T) Homework Equations The Attempt at a Solution a) This one was fine, E(U)=1 b) I...

Homework Statement 1 and 2 take turns shooting at a target. Each time 1 shoots he hits the target with probability p1; 2 hits it with probability p2 each time. 1 shoots first. They stop when the target has been hit twice. What is the probability that... a) The first hit was by 1 ? b) Both...

I've been struggling with this problem for more than 4 days now: Let A, B and C be exponential distributed random variables with parameters lambda_A, lambda_B and lambda_C, respectively. Calculate E [ B | A < B < C ] in terms of the lambda's. I always seem get an integral which is...

Homework Statement We have a bag of n balls, n/2 of which are green and n/2 of which are blue. Consider the following experiment: We reach into the bag and pull out two balls. If they of the same type, we put them both back in the bag. If they are of dierent types we put them both on the...

Homework Statement The masses of suspended particles in a sample of water taken from a lake can be assumed to be a random variable which is normally distributed with mean 2.17 and variance 0.979. Find the probability that out of 4 samples of lake water known to contain less than 1.8 mg of...

Hey All, I've just started reading a discrete math book, and in the beginning the book covers logic. One concept I'm finding hard to understand is certain conditional propositions. When the example uses a word problem, I mostly get it. The statement is "If The Mathematics Department...

Dear all, How can I find the the following conditional probability: f_Y(y/\gamma_f\leq \gamma_0), where Y=\gamma_f+\text{min}(\gamma_h,\gamma_g), where all gammas with subscripts f, g, h are i.i.d exponential random variables. Thanks in advance

P(A|B)=\frac{P(B|A)P(A)}{P(B)} P(B|A)P(A)= \frac{(P(B)\cap (P(A)) P(A)}{P(A)}=P(B)\cap P(A)=P(A)\cap P(B) P(A|B)=\frac {(P(A)\cap P(B))\vee (P(B)\cap P(A))}{P(B)} 0\leq(P(A)\cap P(B))\leq P(A); P(A)\leq P(B) 0\leq(P(B)\cap P(A))\leq P(B); P(B)\leq P(A)

If Y1,Y2,Y2 ~ Multinomial with parameter (n,p1,p2,p3) Prove that the conditional distribution of Y1 given Y3=m (m<n) is a binomial with ( (n-m), p1/(p1+p2) ) p1+p2+p3=1 y1+y2+y3=n y3=m My Attempt: P( Y1=y1| y3=m) = P(Y1=y1, Y3=m)/ P(Y3=m) ( n choose m and y1 ) p1^y1*p3^m / ( n...

I was wondering if there's an example of a power series \sum_n^\infty c_n (z-a)^n with radius of convergence R so that all z for which |z-a| = R there is purely conditional convergence? (no divergence but also no absolute convergence) Or perhaps a reason why that's impossible?

Any advice on how to make step 6 check out?

Homework Statement A truth serum has the property that 90% of the guilty suspects are properly judged while 10% are improperly found innocent. On the other hand innocent suspects are misjudged 1% of the time. If the suspect is selected from a pool of suspects of which only 5% have ever...

Homework Statement I'm currently trying to revise for exams and really struggling on this problem: Suppose you have 3 coins that look identical (ie don't know which is which) with probabilites of 1/4, 1/2 and 3/4 of showing a head. 1. If you pick a coin at random and flip it, what is...

How to compute E[X|Y1,Y2]? Assume all random variables are discrete. I tried E[X|Y1,Y2] = \sum_x{x p(x|y1,y2) but I'm not sure how to compute p(x|y1,y2] = \frac{p(x \cap y1 \cap y2)}{p(y1 \cap y2)} If it is correct, how can I simplify the expression if Y1 and Y2 are iid?

f(x,y) = x + y is the joint probability density function for continuous random variables X and Y. The support of this function is {0 < x < 1, 0 < y < 1}, which means it takes positive values over this region and zero elsewhere. g(x) = x + (1/2) is the probability density function of X...

Hey guys, I'm having a bit of a problem with this question... Homework Statement If X and Y have a bivariate normal distribution with m_X=m_y=0 and \sigma_X=\sigma_Y=1, find: a) E(X|Y=1) and Var(X|Y=1) b) Pr(X+Y>0.5) Homework Equations N/A The Attempt at a Solution...

Homework Statement X and Y two independent random variables with distribution U(0, 1/2). Find the density of (X + Y)2|X - Y > 0 The Attempt at a Solution I was hoping this would be simpler, but somehow I always end up with nothing. The only thing I can work out just fine is that P(X...

Homework Statement So I just took a probability test and I'm having a hard time with the fact that my answer is wrong. I've done some research online and I believe I am correct, I was hoping to get some input. I'm new to using LaTeX so sorry if it's sloppy. Thanks! Problem: Suppose that the...

Hi, 1- Please explain conditional & unconditional mean square error, and their difference. 2- Which one is the solution for minimum MSE estimation? (that is conditional expectation: E \left[ X|Y \right] . I meant which one is minimized by selecting the conditional expectation.) 3- What is...

Homework Statement Hi All, I have a homework question that I would like some hints on. I am given X and Y with uniform densities on [0,2], and Z := X+Y. The end goal is to find E[X|Z]. Now I know I can use symmetry to argue that E[X|Z] = E[Y|Z], and that E[X|Z] + E[Y|Z] = E[Z|Z] = Z, so...

Hi, everyone : I have the following problem: We have 3 dishwashers X,Y,Z, with the conditions: 1) X washes 40% of dishes, and breaks 1% of the dishes s/he washes. 2)Y washes 30% of the dishes, breaks 1% 3)Z washes 30% of the dishes and breaks 3%. Question: If...

Homework Statement Let X and Y be independent and normal, then we know that It must be the case that X+Y and X are jointly normal Therefore we can apply the projection theorem: which states that if A and B are jointly normal then VAR(A|B)=VAR(B)-\rho^2VAR(B) , apply the theorem to A=X+Y, B=Y...

i have a question regarding adsolute and conditional convergence of alternating series. - i know that summation of [ tan(pi/n) ] diverge, but how do we proof it converge conditionally? (ie, (-1)^n tan(pi/n) ] can Leibiniz's theorem be used in this case? but tan(pi/2) is infinite? any...

Hallow! May anyone please help me on conditional probability i actualy understand how it occurs but the formula? The logic behind it! ie P(A/B)=P(AnB)/P(B)

Homework Statement For the random variable X with the following cumulative distribution function: Calculate P(X\leq1.5|X<2), P(X\leq1.5|X\leq2) and P(X = -2| |X|=2) The Attempt at a Solution This is an exercise about a subject I'm yet to see in class, but the teacher asked us to...

I have been stuck at this calculation. There are two exponential distributions X and Y with mean 6 and 3 respectively. We need to find E[y-x|y>x] I keep getting it negative, which is clearly wrong. Anybody wants to try it?

Homework Statement Determine whether the series converges absolutely, conditionally, or not at all. a) \Sigma (-1)nn4/(x3 + 1) b) \Sigma sin(x)/x2 Homework Equations The Attempt at a Solution a) positive series is n4/n3+1 .. do i do comparison test ?? b) |sin(x)|/x2...