Conditional Definition and 447 Threads

Homework Statement Let X_1, X_2, X_3 be iid with common pdf f(x)=exp(-x), 0<x<infinity, 0 elsewhere. Evaluate P(X_1<X_2 | X_1<2X_2)Homework Equations f(X|Y) = f(x,y)/f(y) The Attempt at a Solution Since P(X_1<X_2) is a subset of P(X_1<2X_2), the intersection (edited, at first said union)...

Homework Statement This isn't really homework, just reviewing for a test. This is problem 3.17 in 'A modern introduction to probability and statistics: understanding why and how' Dekking. But since it can be seen as a HW problem, might as well post here. Question: You and I play a...

(please refer to attached image) The question appears to be simple enough, but i have two queries A) does E[X1 X2] mean the same as E[X1 | X2] B) If not/so, how exactly do I go about computing this. I've seen a few formulas in my lectures notes for computing conditional expectations for...

Homework Statement Question 1: A teacher gave his class two tests where every student passed at least one test. 72% of the class passed passed both tests and 80% of the class passed the second test. (i)what percentage of those who passed the second test also passed the first? (ii) what...

I'm just going to post a screenshot of the Example (free online textbook). I'm having a tough time making the leap to the first sum - what allows me to rewrite P(T|A) as the sum of the product of those two conditional probabilities? Thanks

X (n by 1) follows a multivariate normal distribution, i.e., X ~ N(mu, Sigma). mu is n by 1, Sigma is n by n. What is E(X|X_{sub}=A)? where the index 'sub' (m by 1) is a subset of {1,2,..,n}, A is m by 1, 1 <= m < n.

I'm casually working on determining the probability of a team in a given sport (let's say football) reaching at least a certain level in a season. There are two main parts to this: How many games they won in the season, and how far they got in the playoffs. I'd like to assign one final number...

1. Homework Statement +Relevant equations+Attempt at a solution Hi, I'm stuck on a problem. I have that [/itex]P(x,t|y,0)[/itex] represents the probability density that a function has the value x at time t knowing it had the value y at time [/itex]t_0=0[/itex] . Where...

Hello, I have a simple question regarding changing variables in a conditional distribution. I have two independent variables r \in \mathbb{R}, r>0 \\ t \in \mathbb{I}, t>0 where r is "rate" (can be any positive real number although most likely to be around 1) and t is "time" (positive...

Here is a proof question: For two random variables X and Y, we can define E(X|Y) to be the function of Y that satisfies E(Xg(X)) = E(E(X|Y)g(Y)) for any function g. Using this definition show that E(X1 + X2|Y) = E(X1|Y) + E(X2|Y) So what I did was I plugged into X = X1 + X2 E(E(X1 +...

Homework Statement If X1 is uniform on [0,1], and, conditional on X1, X2, is uniform on [0,X1], find the joint and marginal distributions of X1 and X2 Homework Equations conditional joint distribution The Attempt at a Solution f(x1|x2) = 1/x1 (for 0<x2<x1) f(x1) = 1 ( for...

Homework Statement From Mathematical Statistics and Data Analysis 3ed, Rice 1.8 #61 Suppose chips are tested and the probability they are detected if defective is 0.95, and the probability they are declared sound if they are sound is 0.97. If 0.005 of the chips are faulty. What is the...

Hello, I've been working on some questions from Rice's Mathematical Statistics and Data Analysis and I'm not sure about my solutions. The question I'm working on is as follows: 1.8 #59c A box has 3 coins: 1 with two heads, 1 with 2 tails and 1 fair coin. A coin chosen randomly is flipped...

Suppose that there are 2 apple trees. Tree A and tree B. A produces 0.7 of the farm's apples. And B produces 0.3. Out of the apples that tree A produces, 0.15 are bad. For B, 0.05 are bad. One package of goodies contains 3 apples. Given this information, what is the P(Tree A| at...

Help needed. Let A1, A2 and B be events with P(B)>0. Events A1 and A2 are said to be conditionally independent given B if P(A1nA2|B)=P(A1|B)P(A2|B). Prove or disprove the following statement: Suppose 0<P(B)<1. If events A1 and A2 are conditionally independent then A1 and A2 are also...

Hi, I was reading about Markov chains and came across the following statement: "The conditional distribution p(x_n|x_{n-1}) will be specified by a set of K-1 parameters for each of the K states of x_{n-1} giving a total of K(K-1) parameters." In the above we have assumed that the...

we have a variable that takes values 1,...,6 with density: n 1 2 3 4 5 6 f(n) 0.1 0.2 0.1 0.3 0,176 0,124 What is the average price (expected value) of X under the condition that X is even? E(X/X=even)=k*P(X=k/X=even)=0.2*2+4*0.3+0.124*6 i am...

Homework Statement The number of hours of sunshine in one week in a specific resort is assumed to follow a normal distribution with expectation 43 and standard deviation 17. Family A will spend the first three weeks of the summer at the resort. Family B will spend the LAST two weeks of...

Homework Statement We have two normally distributed random variables: A = N(129, 29.4) B = N(86, 24.0) What is the probability A is atleast twice the size of B? The Attempt at a Solution P(A > 2B | B = b) or something? I think we are supposed to use the CLT somehow but I don't...

Homework Statement In 1988, the state of Illinois required HIV testing for a couple to obtain a marriage license. The HIV testing at the time consisted of two separate tests, the ELISA test and the Western Blot test. The Elisa test was signicantly less expensive. A person who is HIV...

Let v be a random variable distributed according to F(.). Let X be a set containing the objects x1 and x2. Suppose E(v|x1) = b AND E(v|x2) = b (The expected value of v conditional on x1 is b, etc) where b is some constant. Does it follow that E(v|x1,x2) = b? If so, why...

Obviously, this is a homework assignment, so I don't want it done for me; however, I am confused. Perhaps I am just confused by the problem or the wording, but I am totally stuck on what to do. I believe the output signal should be a convolution where Z = X + Y, and Y is the gaussian(0, 2)...

Hi, I wish to confirm the results I obtained for the two following questions in statistics. I'd truly appreciate your feedback. Homework Statement 1) Die 1 and die 2 form a pair of unbiased dice. Die 1 has 4 faces painted red and 2 painted blue, whereas die 2 has 4 faces painted blue and 2...

Homework Statement X_t and Y_t are poisson processes with rates a and b n = 1,2,3...Find the CDF F_X{}_t{}_|{}_X{}_t{}_+{}_Y{}_t{}_={}_n(x)Homework Equations The Attempt at a Solution F_X{}_t{}_|{}_X{}_t{}_+{}_Y{}_t{}_={}_n(x) =P(X_t<x|X_t+Y_t=n) =\frac{P(X_t<x,X_t+Y_t=n)}{P(X_t+Y_t=n)} Not...

Homework Statement This is a subset of a larger problem I'm working on, but once I get over this hang up I should be good to go. I have a set of measurements x_n that are exponentially distributed p(x_n|t)=e^{-(x_n-t)} I_{[x_n \ge t]} and I know that t is exponentially distributed as...

It seems weird that such a relatively complex concept is simply given as a definition in most textbooks and then dismissed for further explanation other than using it intact or as a basis for further proofs.

Hi, I have a general concept question. I am working with finding complete sufficient statistics of distributions. Sometimes I need to condition some function of a parameter on a sufficient statistic, using basically Rao-Blackwell, but my trouble is in finding the conditional distributions...

Homework Statement A population has n men and n women. If you where to take 4 people out of the population to form a group what's the probability that there are exactly the same number of men as women in the group . Homework Equations The Attempt at a Solution Ok so I thought...

Okay so I have a complex setup that I hope I can convey. I have 9 sites to which X can bind. 6 out of the 9 sites are active and 3 out of the 9 sites are inactive. I need 3 of the active sites to be bound to get the response I am looking for - which we will call EMAX. So when I add a...

Hi, I am trying to show that if the E[W|X]=0 then the Cov (W,X)=0. Using the def of variance, and given that E[W] is zero, I get that Cov is equal to: E[WX]-E[W * E(X)] using conditional expectation: E [E(WX|X)] -E[x]E[W]= E[X E[W|X]]-E[X]E[E(W|X)]=0 I am not sure if...

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" OR Say I flip a quarter. Would the...

1. Assume that there is a 50% chance of hard drive damage if a power line to which a computer is connected is hit during an electrical storm. There is a 5% chance that an electrical storm will occur on any given summer day in a given area. If there is a 0.1% chance that the line will be hit...

So,I'm studying statistics (for engineers) now,and this is one of them courses that really gives me a headache time after time. Here for example,I can't seem to get the difference between P(A\bigcapB),and P(A|B).I'l give an example in for of a question given to us in some class. "70 percent...

I computed the distribution of B_s given B_t, where 0\leq s <t and \left\{B_t\right\}_{t\geq 0} is a standard brownian motion. It's normal obviously.. My question is, how do I phrase what I've done exactly? Is it that I computed the distribution of B_s over \sigma(B_t)?

My professor made a rather concise statement in class, which sums to this: E(Y|X=xi) = constant. E(Y|X )= variable. Could anyone help me understand how the expectation is calculated for the second case? I understand that for different values of xi, we'll have different values for the...

What is prob of 0 in ASCII text file assuming it is bit string? Analysis: MSB(1st bit in each byte) is always 0. So Pr(MSB) = 1/8. its space is 2^7=256. Assuming each character is randomly distribution(same ratio of appearing in text), besides MSB, other bits follow the rule Pr(0)=Pr(1)=1/2...

Homework Statement Suppose the distribution of X2 conditional on X1=x1 is N(x1,x12), and that the marginal distribution of X1 is U(0,1). Find the mean and variance of X2. Homework Equations Theorem: E(X_{2})=E_{1}(E_{2|1}(X_{2}|X_{1}))...

Homework Statement A certain delivery service offers both express and standard delivery. Eighty-five percent of parcels are sent by standard delivery and 15% are sent by express. Of those sent standard, 80% arrive the next day, and of those sent express, 95% arrive the next day. A record of...

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...

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...

[FONT=Lucida Grande]Assume two random variables X and Y are not independent, [FONT=Lucida Grande]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? [FONT=Lucida Grande]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...