Conditional Definition and 447 Threads

I am trying to iterate a solution to a non-linear differential equation - but I am unable to evaluate a statement within a Do loop Code: Do[q = Cos[Evaluate[x'[i]/.up]]; If[ q <= 1, Print[q], Print[i], Print[i^2]], {i, 0.1, 1, .1}] x'[i] is a solution to NDSolve The output is i^2, which is...

If I have x1,x2 iid normal with N(0,1) and I want to find E(x1*x2 | x1 + x2 = x) Can I simply say: x1 = x - x2 and thus E(x1*x2 | x1 + x2 = x) = E[ (x - x2)*x2) = E[ (x * x2) - ((x2)^2) ] <=> x*E[x2] - E[x2^2] = 0 - 1 = -1?

Homework Statement One satellite is scheduled to be launched form Cape Canaveral in Florida, and another launching is scheduled for Vandenberg AFB in California. Let A denote the event that the Vandenberg launch goes off on schedule, and let B represent the event that the Cape Canaveral...

Homework Statement Components of a certain type are shipped to a supplier in batches of ten. suppose that 50% of all such batches contain no defective components, 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected...

Homework Statement I want to write the following if statement into simply manipulations using the bit operations: ! ^ & | << >> ~ + Given an x... if ( x == -1 || x == 0) return -1; else return 0; I am dealing with 32-bit integers. How do I go about doing this? (Note: -1 is...

Homework Statement I'm told that of n couples, each of whom have at least one child, with couples procreating independently and no limits on family size, births single and independent, and for the ith couple the probability of a boy is p_i and of a girl is q_i with p_i + q_i = 1. 1. Show...

My questions I am looking at is: We have twelve balls, four of which are white and eight are black. Three blindfolded players, A, B, and C draw a ball in turn, first A, then B, then C. The winner is the one who first draws a white ball. Assuming that each black ball is replaced after being...

Hi all, I've got this very simple problem: I know it is an elementary problem, but I never really got into that bayes' theorem, which I need to use here, right? I would be grateful for simple and plain explanation. thanks for your time, rahl.

The problem is stated as follows: You have an urn with 12 red balls, 20 green balls, and 13 yellow balls. Suppose 3 balls are drawn without replacement. What is the probability the third ball is yellow given the first ball is green. I am pretty sure I use Bayes formula, but I am not certain...

Given X follows an exponential distribution \theta how could i show something like \operatorname{E}(X|X \geq \tau)=\tau+\frac 1 \theta ? i have get the idea of using Memorylessness property here, but how can i combine the probabilty with the expectation? thanks. casper

How can I do this? Let X,Y r.v., \mathbb{E}(X|Y)=Y and \mathbb{E}(Y|X)=X. Proove that X=Y a.s.

Homework Statement Chose a point at random in a square with sides 0<x<1 and 0<y<1. Let X be the x coordinate and Y be the y coordinate of the point chosen. Find the conditional probability P(y<1/2 / y>x). Homework Equations No clue. The Attempt at a Solution Apparently, according...

An event A has a 70% chance of occurring, an event B has a 40% of occurring and the event (A n B) has a 20% chance of occurring. The events are not unrelated. If A does not occur what is the probability of B? notation A' means (not A) I have tried to use the formula P(B|A') = P(B n...

Homework Statement A baseball player compiles the following information : He hits a home run in 34% of his games He gets a strike out in 40% of his games In 78% of his games he hits a home run or his team wins In 10% of his games he hits a home run and gets a strike out In 26% of his...

Homework Statement There are w white balls and b black balls in a bowl. Randomly select a ball from the bowl and then return it to the bowl along with n additional balls of the same color. Another single ball is randomly selected from the bowl(now containing w+b+n balls) and it is black. Show...

Homework Statement A couple has two children. What is the probability that both are girls given that the oldest is a girl? What is the probability that both are girls given that one of them is a girl? DO NOT assume that female births and male births are equally likely. Assume identical...

Homework Statement A concrete beam my fail by shear or flexure. The failure probability in shear is equal to the failure probability in flexure, and the probability of failure in shear when the beam is loaded beyond is flexure capacity (ie, it has already failed in flexure) is 80%. Find the...

Conditional Probability... My handout says this... P(m) = .4 P(w) = .5 P(m|w) = .7 Find: P(MnW) = ? P(w|m) = ? P(m or w) = ? P(MnW) = .4 x .5 = .2 P(w|m) = .35/.4 = .875 P(m or w) = ?

I've been struggling for a good couple hours on the below, and I was hoping someone might be able to push me in the right direction... "A" represents the event "the breath analyzer indicates the suspect is drunk" and "B" represents the event "the suspect is drunk." On a given Saturday night...

Hi I'm trying to convince myself that the conditional entropy of a function of random variable X given X is 0. H(g(X)|X)=0 The book I'm reading (Elements of Information Theory) says that since for any particular value of X, g(X) is fixed, thus the statement is true. But I don't...

Hey! I need to perform the following integration: \int\limits_0^{\infty} J_1(k r)k dk where J_1(x) is the cylindrical Bessel function of the first kind. This is an oscillatory function with amplitude decreasing as 1/\sqrt{x}. Due to the multiplication of k the integrand however, becomes...

If a hand of 5 cards are dealt from a 52 card pack (order doesn't matter), what is the probability that the hand will contain the ace of spades GIVEN that there is at least one ace? Thanks.

Homework Statement A particular brand of cars, say ABC, comes in only two colours, white and grey. Exactly 90% of ABC cars in a particular town are white and 10% are grey. Mrs Z, a witness to a bank robbery, claims to have seen the thieves escaping in an ABC grey car, which taking into...

Homework Statement Given f(x) = e^-x and f(y|x) = 1/x e^(-y/x). Three parts: (a) Compute density of (x,y), (b) Compute E(y) and (c) Compute P(y>x). Homework Equations f(x,y) = f(y|x)f(x) if f(x) = ve^(-vx), then E(x)=v^(-1) The Attempt at a Solution I'm stuck on a problem. I was...

I'm stuck on a problem. I was given f(x) and f(y|x) and was able to derive f(x,y). The second step of the problem is computing P[y>x]. I think I need to know f(y) to answer this problem but I can't figure out how to derive it. Or is there a way to compute P(y>x) given the info I know without...

Hello everybody, I have two questions on conditional expectation w.r.t (Polynomial) OLS: Let X_t be a random variable and F_t the associated filtration, Vect_n{X_t} the vector space spanned by the polynomials of order {i, i<=n }, f(.) one function with enough regularity. I am wondering how...

I'm having trouble with one of the rules of probability P(A n B) = P(A)P(B) which holds if events A and B are independent The following problem illustrates my confusion. I've defined Events A and B below, are these events dependent? Per the solution in the book P(A \cap B) = P(A)P(B)...

Homework Statement Show the semantic tree of: \neg ( ( p_0 \rightarrow p_1 ) \rightarrow \neg ( p_1 \rightarrow p_2 ) ) Homework Equations \neg ( ( p_0 \rightarrow p_1 ) \rightarrow \neg ( p_1 \rightarrow p_2 ) ) The Attempt at a Solution I cannot understand its purpose...

Homework Statement a family consisting of a father, mother, and a child is chosen at random and is asked on what day of the week each of them was born. What is the probability that all three were born on different days given that the father was born on a monday? Solution: A is the even all...

I am learning how to prove conditional identities like (a^2-c^2+b^2+2ab)/(c^2-a^2+b^2+2bc) = (s-c)(s-a) if a+b+c = 2s - Derived from Herons formula I have understood the proof for the above , but i want more problems to work on. Can anyone suggest some link where i can find similar...

Homework Statement Suppose a person's score X on a math aptitude test is a number between 0 and 1, and their score Y on a music aptitude test is also between 0 and 1. Suppose further that in the population of all college students in Canada, the scores X and Y are distributed according to the...

This result isn't in our book, but it is in my notes and I want to make sure it's correct. Please verify if you can. Homework Statement I have two I.I.D random variables. I want the conditional expectation of Y given Y is less than some other independent random variable Z. E(Y \...

Please help me with this. Any suggestions are greatly appreciated. Imagine that I have a bank account. X is the amount of cash on the account at time t+1. Y is the amount of cash at time t. The amount of cash depends on the deposits made and on the amount of cash during the previous period...

This is probably relatively easy, but I'm still a bit confused... The question: A family has j children with probability p1 = .1, p2 = .25, p3 = .35, p4 = .3. A child is randomly chosen. Given this child is the eldest in the family, find the conditional probability that a) Family has 1...

Homework Statement boy and girl independently flip each a biased coin with probability of heads p1 for boy, and p2 for girl. they record the number of flips needed until heads shows up. what is the probability that they tie? Homework Equations I just know that we should define a...

Homework Statement Test the series for (a) absolute convergence, and (b) conditional convergence. \sum\left(-1\right)^{k+1}\frac{k^{k}}{k!} Homework Equations The Attempt at a Solution So I tried taking the absolute value and then applying the ratio test, which, after...

Hello, This question relates to Bayes law. I think my problem is I am not sure of the name of the thing I am trying to derive... I have 2 variables a and b. a = 1 or 0, b = 0...n I have the data to calculate; p(a = 1 and b) p(b) for any b. Hence I can find p(a=1|b) = p(a = 1 and...

hi all, I have a question that i really want to know the answer. the probability that an airplane will return in 10min is 30%, in 20min is 30%, in 30min is 0%, in 40min is 40% according to the past history records. given that the airplane has not return in 20min, what is the probability...

I need help about conditional expectation for my research. I get stucked on this point. Could anyone show me how to prove that: "Let E[|Y|]<∞. By checking that Definition is satisfied, show that if Y is measurable F0, then E[Y|F0]=Y." Def: Let Y be a random variable defined on an underlying...

I am new in MATLAB and recently, I have tried coding in matlab. So far, I have been getting error msg "Warning: Failure at t=2.859413e+002. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.015868e-012) at time t." I have referred...

Hi, I am a quantum physicist who needs a practical help from mathematicians. :smile: The physical problem that I have can be reduced to the following mathematical problem: Assume that we have two correlated variables a and b. Assume that we know all conditional probabilities P(a|b), P(b|a)...

Dear all, Please clarify the following: 1.) The difference of conditional probability and Bayes' formula. 2.) Is Bayes' formula a "all weather condition" formula for all conditional probabilities problem? Thank you, S

what is conditional rule,how is it used in: 1) propositional calculus 2) IN ordinary mathematical proofs ,examples will help

Dear all, P (A |B) + P (A c|B) = 1 [A c] denotes complement of set A and of course P (B)>0 Is the above statement true? How about the following two: P (A |B) + P (A |B c) = 1 P (C ∪ D|B) = P (C |B) + P (D|B) − P (C ∩ D|B)

Homework Statement In a shipment of 100 televisions, 6 are defective. If a person buys two televisions from that shipment, what is the probability that both are defective? Homework Equations the Answer is somewhat weird! it says it is 1/330 ! which is really beyond by recognition...

I ran across this identity for a conditional PDF where the dependent random variable X is continuous and the independent variable N is discrete: \frac{P(x<X<x+dx|N=n)}{dx}=\frac{P(N=n|x<X<x+dx)}{P(N=n)}\frac{P(x<X<x+dx)}{dx} In the limit as dx approaches 0 this yields: f_{X|Y}(x|n)...

Hi, I'm trying to work out a probability value from a number of distributions (tests), it gets a little complicated because some of the tests are dependent on each other. Lets say I have a surface which has black and white regions distributed over it, where black is "true" and white is "false"...

I'm trying to solve a problem as part of my research and it's giving me fits. It seems like it should be simple, but I can't wrap my brain around how to do it. The problem is: Suppose X~N(0,s), and Y is a random variable that has a probability mass point at 0 but is otherwise uniformally...

Although this problem may look like homework, I assure you it is not. It is a question that arose from a trading card game that I am stuck on. The problem is as follows (with simplified cards) You have a deck of 53 cards, and 11 of those cards are red and 42 are black. If you were to randomly...

I'm supposed to calculate the cost of renting a Ford, Cadillac or Toyota, and use conditional statements to calculate the different costs of each vehicle. users are supposed to enter “F” for Ford, “T” for Toyota, or “C” for Cadillac users enter “F” for Ford, “T” for Toyota, or “C” for Cadillac...