Conditional Definition and 483 Threads

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...

Hi: e, z, mu are vectors of size N I need to show that E(e|z+mu) = E(e|mu) or at least E(e|z+mu) converges in probability to E(e|mu) as N goes to infinity, under the assumption that Z is not correlated with e. My guess is that to get this result I also need z to be orthogonal to mu...

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)...

There are 15 tennis balls in a box, of which 9 have NOT previously been used. Three of the balls are randomly chose, played with, and then RETURNED TO THE BOX. Later, another 3 balls are randomly chosen from the box. Find the probability that none of these balls has ever been used. Seems...

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)...

Suppose X1 Y1 Z1 0 0 0 (5 times Z1 is 0 for X1=0 and Y1=0) 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 . . . Which is.. (Same table which is above..) X1 Y1 Z1 (Count of Zeros) (Count of...

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...

Homework Statement Let Z_1, \ldots, Z_n be independent standard normal random variables, and let [tex]S_j = \sum_{i=1}^j Z_i[/itex] What is the conditional distribution of S_n given that S_k = y, for k = 1, ..., n? The attempt at a solution I know that S_j is a normal random...

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...

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...

Homework Statement Let (X_n; for all counting number n) be a sequence of independent random variables. We focus on the random walk S_n := X_1 + . . . + X_n and set F_n = 'sigma-algebra' of (S_1, . . . , S_n). 1. Compute E[S_(n+1) \ F_n] 2. For any z belonging to the complex plane C...

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...