Conditional Definition and 483 Threads

Homework Statement I flip a coin 10 times and want to know the probability of getting exactly 7 heads given that the first flip is heads. The Attempt at a Solution The question above is part of a larger question involving the binomial RV, but I am only needing assistance here. Using...

Suppose that α and β are independently distributed random variables, with means; μ_α, μ_b and variances; δ_α^2, δ_β^2, respectively. Further, let c=αβ+e, where e is independently distributed from α and β with mean 0 and variance δ_e^2. Does it hold that E(αβ | c) = E(α|c)...

Homework Statement You start out with a bag that contains either a red marble or a green marble with equal probability. Then, a red marble is added to the bag. If I draw out a red marble the first time, what is the probability of drawing out a green marble the second time? Homework...

I've written a modified mutation algorithm that I am trying to derive a more analytical probability model for. The basic algorithm works like this: 1. The probability of mutation is P(M) = 0.01. 2. If mutation occurs, then: a. The probability that mutation-type A is P(A|M) = 0.50 b. The...

Scope of this thread is to give a complete as possible answer to the question proposed two days ago by the user simon11 on Basic Probability and Statistic forum... Assume two random variables X and Y are not independent, if P(X), P(Y) and P(Y|X) are all normal, then does P(X|Y) also can only be...

Hi all, While solving problems related to probability I got stucked with this problem: In some election 4 candidates A,B,C,D has the probability of being elected is 0.4,0.3,0.2,0.1 respectively.If the candidate C discard his candidateship just prior to the election ,then what will be the...

Assume two random variables X and Y are not independent, if P(X), P(Y) and P(Y|X) are all normal, then does P(X|Y) also can only be normal or not necessarily? thanks.

Homework Statement A standard deck of 52 cards of 4 suits, each with 13 denominations, is well shuffled and dealt out to four players, N, S, E and W, who each receive 13 cards. If N and S have exactly ten cards of a specified suit between them, show that the probability that three remaining...

Anyone know answer to below. If two random variables X and Y are both marginally normal, and conditional distribution of Y given any value of X is also normal. Does this automatically mean the conditional distribution of X given any value of Y also has to be normal? or not necessarily.

Homework Statement Suppose we have 10 coins such that if the ith coin is flipped, heads will appear with probability i/10, i = 1,2...10. When one of the coins is randomly selected and flipped, what is the conditional probability that it was the coin? Homework Equations Bayes's Formula...

Homework Statement 1) S'pose we flip 2 fair coins, and roll one fair 6 sided die. What is the probability that the number of heads equals the number showing on the die? 2) We roll 4 fair six sided dice. What is the conditional prob. that the first die shows 2, conditional on the event that at...

Homework Statement Consider 3 urns. Urn A contains 2 white and 4 red balls, Urn B contains 8 white and 4 red balls and Urn C contains 1 white and 3 red balls. If 1 ball is selected from each urn, what is the probability that the ball chosen from urn A was white given that exactly 2 white...

A Box contains black balls and white balls, with 1/2 of each. Now we add black balls, with 1/8 of total. What is probability of drawing 1 black, 2 black and 3 black balls respectively (no replication)? Analysis: Drawing one black ball : 1/8*1/2+1/2 = 9/16. Thinking of conditional...

Homework Statement We are given a belief network such that the overall joint probability after accounting for conditional independence is: P(a,b,c,d,e) = P(a)P(c|a,b)P(d|b)P(e|d,b) The values provided are: P(a = false) = .02 P(b = false) = .95 P(c= false|a=true, b=true) = .97 P(c=...

What I mean by this is, Say I roll a die, given the specific condition that I get four eights consecutively such as "8888", the same probability as if I give the specific condition that I get another specific non-consecutive number such as? "0248" Thanks

1. Given f(x,y) = 2, 0<x<y<1, show V(Y) = E(V(Y|X)) + V(E(Y|x)) Homework Equations I've found V(Y|X) = \frac{(1-x)^2}{12} and E(Y|X) = \frac{x+1}{2} The Attempt at a Solution So, E(V(Y|X))=E(\frac{(1-x)^2}{12}) = \int_0^y \frac{(1-x)^2}{12}f(x)dx, correct?

Bob picks 3 cats. There are 5 striped males, 6 striped females, 8 spotted males, and 4 spotted females. What is the prob. that Bob has atleast a striped cat given that he has picked at least a female? ------------------------------------------------------ I have: (prob. of a striped...

A conditional statement is of the form A→B. Truth tables suggest that the converse, B→A ≠ A→B. It is also known that any two vectors A and B are perpendicular if and only if their dot products are zero. My confusion is... A dot B = 0 → A and B are perpendicular. The converse is...

1. You give a friend a letter to mail. He forgets to mail it with probability 0.2. Given that he mails it, the Post Office delivers it with probability 0.9. Given that the letter was not delivered, what’s the probability that it was not mailed? 2. I assume I'm supposed to use Bayes...

Hi there, I have the journey times of 2 journeys. Would somebody be able to show me by way of example how to calculate the conditional probability function of the second journey time given the first journey time? https://dl.dropbox.com/u/54057365/All/jt.JPG Appreciate your help Thanks John

1. Let the joint pdf be f(x,y) = 2 ; 0<x<y<1 ; 0<y<1 Find E(Y|x) and E(X|y)Homework Equations E(Y|x) = \int Y*f(y|x)dy f(y|x) = f(x,y) / f(x) The Attempt at a Solution f(x) = \int 2dy from 0 to y = 2y f(y|x) = f(x,y)/f(x) = 1/2y E(Y|x) = \int Y/2Y dy from x to 1 = \int 1/2 dy from x to 1 =...

Hi all, I need help regarding the following expression: E(x1|X>K) where: x1 is a one dimension normal rv X is multivariate normal rv with n components: x1, x2,..., x_n K is a n dimension constant vector with n components: k1,k2,...,k_n X>K <==> x1>k1,x2>k2,...,x_n>k_n I know there is...

Homework Statement Of the items produced daily by a factory, 40% come from line I and 60% from line II. Line I has a defect rate of 8%, whereas line II has a defect rate of 10%. If an item is chosen at random from the day’s production, find the probability that it will not be defective...

My probability class has me wondering about pure math questions now. We started with the axioms and are slowly building up the theory. Everything was fine but then a definition of Conditional Probability P[A|B] = \frac{P[AB]}{P[B]} appeared and it's just not sitting right with me. I know that...

P(S1 \cap S2 \cap S3 | r) How do I simplfy the above equation if S2 and S3 are independent of r ?

I have some problems getting conditional probability right... Does this look like it should? Homework Statement Assume that there are bags of tulip bulbs in the basement, ant that they contain 25 bulbs each. yellow bags contain 20 yellow tulips and 5 red tuplips, and red bags contain 15 red...

Hi guys, assume we have an equality involving 2 random variables U and X such that E(U|X) = E(U)=0, now I was told that this assumption implies that E(U^2|X) = E(U^2). However I'm not sure on how to prove this, if anyone could show me that'd be great!

NOT talking about nonabsolute vs absolute convergence. I'm talking about conditional convergence. In my analysis text, this was a bit that was covered as enrichment and it straight up blew my mind. I don't get it. How can you simply rearrange terms and come up with a separate sum? They showed a...

1. I am going over some past Probability exam papers and cannot solve this question. Any help or advice would be much appreciated! 2. David eats cereal for lunch 60% of days. If he had ice cream for breakfast, then the probability that he eats cereal for lunch is only 0.25. If he didn't...

I am working on studying for a probability exam and I just came across conditional variance, but I can't find anything in my materials for how to solve it. If I want to find the conditional variance of Y given that X=x, or Var[Y|X=x], how would I solve it? I am given a continuous distribution...

I am working on studying for a probability exam and I just came across conditional variance, but I can't find anything in my materials for how to solve it. If I want to find the conditional variance of Y given that X=x, or Var[Y|X=x], how would I solve it? I am given a continuous distribution...

Homework Statement Given X,Y RV both have normal distribution with: μ_{x}=6,μ_{y}=4,σ_{x}=1,σ_{y}=5,ρ=0.1 a. are X,Y independent? b. find P(X≤5) c. find P(Y≤5|X=5) 2. The attempt at a solutiona. no -> ρ=0.1 -> cov(X,Y)≠0 b. define Z=\frac{X-6}{1} ; Z~N(0,1) so P(X≤5) = P(Z≤-1) = \Phi(-1)...

Homework Statement Suppose you have 3 nickels and 4 dimes in your right pocket and 2 nickels and a quarter in your left pocket. You pick a pocket at random and from it select a coin at random. If it is a nickel, what is the probability that it came from your right pocket? 2. The attempt at a...

You are given a random exponential variable X: f(x) = λ exp(-λ x). Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X: Y = IP(X), Z = FP(X). Which is the following conditional probability: P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?

Hello, I'm trying to work out a conditional probability. I have hundreds of measurements of two variables (1) Start Time and (2) Journey time. I've created a frequency table. https://dl.dropbox.com/u/54057365/All/forum.JPG How can I work out the Journey time given a start...

Hello, I'm trying to work out a conditional probability. I have hundreds of measurements of two variables (1) Start Time and (2) Journey time. I've created a frequency table. https://dl.dropbox.com/u/54057365/All/forum.JPG How can I work out the Journey time given a start time? P(JT |...

Hi, all. I happened to think about a problem about conditional PDF: x_2=x_1+a, x_1 \approx \mathcal{N}(0,1), a \approx \mathcal{N}(0,1) so the conditional PDF of f(x_2|x_1), f(x_1|x_2) would both be f(x_2|x_1)=f(x_1|x_2)=\frac{1}{\sqrt{2\pi}}\exp{(-\frac{(x_1-x_2)^2}{2})} And it is clear...

Homework Statement The Attempt at a Solution I have that the joint probability mass function would be \Pi_{i=1}^{k} \frac{\lambda_{i}^{n_{i}}}{n_{i}!} e^{-\lambda_{i}} How would I go about applying the conditional to get the conditional distribution?

Hi all, My question is the following. Let's say I have two probability distributions; f(x|b)\,g(x|c) b and c are discrete events while x is a continuos variable. i.e When the button b is pressed there is some distribution for the amount of rain fall the next day, x. When the button c...

Need help A system contains two components A & B. The system will function so long as either A or B functions. The probability that A functions is 0.95, the probability that B functions is 0.90, & the probability both function is 0.88. What is the probability that the system functions.

f[x_] := x^2 + c; y = Solve[f'[f[x]] == 1, x, Reals] output: {{x -> ConditionalExpression[Root[-1 + 4 c #1 + 4 #1^3 &, 1], c > -(3/4) || c < -(3/4)]}, {x -> ConditionalExpression[Root[-1 + 4 c #1 + 4 #1^3 &, 2], c < -(3/4)]}, {x -> ConditionalExpression[Root[-1 + 4 c...

T ≡ "two coins tossed 7 times by two people A and B giving outcomes [A^+B^+, A^-B^+, A^+B^-, A^-B^+, A^+B^+, A^-B^-, A^-B^+], where + = heads and - = tails" Calculate P(A^+B^+|T), P(A^+|T), P(B^+|T) and P(B^+|T,A^+) I asked this question elsewhere and there was a suggestion that the question...

Homework Statement The Attempt at a Solution a) P(Pickwick has no umbrella | it rains) = \frac{\frac{1}{3}\frac{1}{3}}{\frac{1}{2}} = \frac{2}{9}, which is the answer according to my answer key. b) For part b we have: There is a rain forecast which means he will bring the...

Homework Statement Compute P(X=k l X+Y=p)Homework Equations The Attempt at a Solution No idea. Kind of understand page #1. Although it seems like there's a lot of unnecessary stuff. Could have gone straight from the top to the bottom. And I don't know why/if you even have to substitute the...

My professor explained this concept absolutely horribly and I have no idea how to do these problems. Let A and B be independent Poisson random variables with parameters α and β, respectively. Find the conditional expectation of A given A + B = c. (Hint: For discrete random variables, there...

Homework Statement What is the expected number of flips of a biased coin with probability of heads 'p', until two consecutive flips are heads?Homework Equations The Attempt at a Solution Let T_1 = first flip is tails, H_1 = first flip is heads. and T_2, H_2 for second flip. \mathbb{E}[X] =...

At the bottom of the page (example 2) for question c) P(B|A'). They say P(B n A') = 0.2. But surely it is (B while not A) which in my mind should be 0.15. Can somebody tell why it is 0.2?

Homework Statement I've spent a few hours but unable to work out the solution of the following questions successfully. The question is as follows: I am having problems with (a)(iii) and (b)(ii) Homework Equations The Attempt at a Solution (a)(iii) Although I can work...

Guys my question should be easy but I cannot understand how it works, here is how it goes. A murder case involves the death of a guest at a large party in a country house. The police are certain that there is only one murderer who is among the N = 100 remaining people in the house. However...

Homework Statement An image of the assigned problem is here: http://imgur.com/aYkaM Homework Equations The formula for being exponential, gamma, and probably Bayes's Law. They'd take a while to type out, and presumably anyone who can help me with this already knows the formulas or...