Conditional Definition and 447 Threads

I was able to do the first part of this problem but unsure how to approach this: Mendel, revisited: Mendel’s peas had either purple or white flowers; flower color is due to a single gene, for which the purple allele (A) is dominant to the white allele (a). We cross two pure-breeding lines...

Homework Statement All athletes at the Olympic games are tested for performance-enhancing steroid drug use. The imperfect test gives positive results (indicating drug use) for 90% of all steroid-users but also (and incorrectly) for 2% of those who do not use steroids. Suppose that 5% of all...

Homework Statement A manufacturer of scientific workstations produces its new model at sites A, B, and C; 20% at A, 35% at B, and the remaining 45% at C. The probability of shipping a defective model is 0.01 if shipped from site A, 0.06 if from site B, and 0.03 if from site C. A- What is...

Homework Statement Two computers are connected to a password-protected wireless network. When the password is temporarily removed, a virus can attack the first computer with probability 0.5, the second computer with probability 0.7, and it can attack both computers with probability 0.4. The...

Homework Statement I've attached both the problems into one image to make life easier since problem 1 has a diagram and the other does not. Homework Equations Bayes Theorem : P(A|B)P(B) / [P(A|B)P(B) + P(A|B')P(B')] B' = B Complement The Attempt at a Solution well for the first one i don't...

Hello, I am stuck with the following question. 1. Suppose T ind. C |Z, does it follow that T ind. C ? 2. Suppose T ind. C , does it follow that T ind. C |Z? I think both don't follow, but I don't know how to show it Thanks in advance

Homework Statement You have 3 urns: Urn 1 has 3 red balls, Urn 2 has 2 red balls, 1 blue ball. Urn 3 has 2 red balls 2 blue balls. You pick a ball from each urn and place it into Urn 4. You draw 2 balls from Urn 4 and they are red. What is the conditional probability that the 3rd ball is also...

A number is selected randomly from a container containing all the integers from 10 to 50 find a) p(even|greater than 40) b) p(greater than 40| even) c) p(prime| between 20 and 40) please provide an explanation, thanks a lot =D

Please, help me to solve the problem Details at a factory are tested randomly to check if they are faulty. It is known from previous experience that the probability of a faulty detail is known to be 0.03. If a faulty detail is tested the probability of it testing faulty is 0.82. If a non-faulty...

Hey guys, first of all I want to say hey to all! I have been a long time lurker and follower of these forums and have been known to find a lot of your answers helping me out throughout my college life. I also know that you just don't like to spit out the answers for those who don't put in...

Two coins are flipped and the results are recorded. Given that one coin lands on a head, find the probability of: a) Two heads, b) a head and a tail Searching online is giving my answers which are not using conditional probability at all, and our teacher told us we have to use the...

I was reading this article of wikipedia: Conditional and absolute convergence It says: "An absolutely convergent sequence is one in which the length of the line created by joining together all of the increments to the partial sum is finitely long." Is that a characterization of...

Product Testing A supposed coffee connoisseur claims she can distinguish between a cup of instant coffee and a cup of drip coffee 75% of the time. You give her 5 cups of coffee and tell her that you will grant her claim if she correctly identifies at least 4 of the 5 cups. (a) What are her...

1. Homework Statement ******* SOLVED ********* There are three magazines A,B and C respectively. A survey of readers was taken and the following data was collected. 0.6 Read A 0.5 Read B 0.5 Read C 0.3 Read A&B 0.2 Read B&C 0.3 Read A&C 0.1 Read A&B&C What is the probability that a reader...

I have a question about the ratio test. Suppose it proves inconclusive, we must than use another test to check for conditional convergence - 1) this test has to be associated with an alternating series, such as the Alternating Series Test, correct? (we wouldn't be able to use something like...

The random variable X has the PDF fX(x) = cx^-2 if 1 < x < 2; 0 otherwise: (a) Determine the value c (b) Let A be the event fX > 1.5. Calculate the conditional expectation and the conditional variance of X given A. I'm not understanding the concept of conditional pdf's. Can someone show me the...

Homework Statement I have two kids. Given that at least one of them is a girl, what is the probability that they are both girls? Homework Equations The Attempt at a Solution I think it's 1/3, because the possibilities are: Boy Boy, Boy Girl, Girl Boy, Girl Girl. There are three...

Hello, I'm somewhat confused by the expression f(X = x | Y = y) = \frac{f(X=x)}{f(Y=y)} (which, if I'm right, is the definition of a conditional probability density? My course seems to state it as a theorem, without proof, but then again my course is a little bit vague; although I welcome...

My book tries to illustrate the conditional expectation for a random variable X(\omega) on a probability space (\Omega,\mathscr F,P) by asking me to consider the sigma-algebra \mathscr G = \{ \emptyset, \Omega \}, \mathscr G \subset \mathscr F. It then argues that E[X|\mathscr G] = E[X] (I'm...

Hello, I want to compute the conditional entropy H(A | B,C), given probability distributions for each of the variables. It would be nice to have a right-hand side not involving conditionals. H(A|B) = H(A,B) - H(B) but how does it work out if there are more than one conditional variable...

1) I'm trying to prove that two R.V.s X & Y are related iff Y & X are related. Assuming they are discretely distributed. So basically from what I've learned is that two R.V.s are related if the joint pdf changes as Y changes. So basically if f(X|Y=yi) changes when i changes. So from that...

need urgent help with a conditional variance proof. I have been given this problem and I'm pretty stumped. I want to prove that Y=g(X) if and only if var(YlX) = 0. so if var(YlX)=0 then E(Y^2lX) - E(YlX)^2 = 0 E(Y^2lX) =E(YlX)^2 so what should I do now? I tried showing that this...

I have a simple-seeming question on conditional expectation. It seems simple, but it has eluded my attempt to answer. Suppose that two jointly distributed random variables (X,Y) exist with support on positive real line. From these, it is possible to construct a new random variable, Z=E[X|Y]...

Homework Statement Basically, I'm given the probability of 4 independent events: P(A) = 0.04 P(B) = 0.03 P(C) = 0.02 P(D) = 0.01 If anyone of these occur, a failure will happen. More than one can happen at the same time. I need to find the probability that more than one of them...

Homework Statement D = (L + E) / S Where L, E, and S are mutually independent random variables that are each normally distributed. I need to find (symbolically), the conditional PDF f(d|s). Homework Equations The Attempt at a Solution Not sure what to do with so many...

Homework Statement A bowl contains 10 chips: 6 red chips and 4 blue chips. three chips are drawn at random and without replacement. Compute the conditional probability that a) 2 are red and one is blue; given that at least 1 red chip is among the 3 selected b) all are red, given that at least...

Homework Statement You are a member of a class of 18 students. A bowl contains 18 chips: 1 blue and 17 red. Each student is to take 1 chip from the bowl without replacement. The student who draws the blue chip is guaranteed an A for the course. a)If you have the choice of drawing first...

Homework Statement An urn contains four colored balls: two orange and two blue. Two balls are selected at random without replacemen, and you are told that at least one of them is orange. What is the probability that the other ball it orange? Homework Equations Now, we have been...

Homework Statement romeo proposed to juliet. now he's waiting for her response. R = 'event that she replies' W='event that she wants to get married' Mon = 'event on monday' Tue = 'event on Tuesday' P(R\wedgeMon | W) = 0.2 P(R\wedgeTue | W) = 0.25 P(R\wedgeMon| \bar{W}) = 0.05...

Hi everyone, I have a feeling the following property is true but I can't find it stated in any textbook/online reference. Maybe it's not true... Can someone verify/disprove this equation? E(A+B|C) = E(A|C) + E(B|C)

Homework Statement I was wondering if anyone knows of a conditional statement that will prevent users from imputing non integer inputs. like for example z=0 while z<1 x=input('Enter Something') if SOME MAGICAL CONDITIONAL STATEMENT disp('You entered a invalid...

Homework Statement given an = ( -1 )(n+1) / \sqrt{n} determine if the infinite series is Absolutely Convergent, Conditionally Convergent, or Divergent. Homework Equations I hope I have these theorems down correctly, please correct me if I'm wrong. If \Sigma|an| is Convergent then...

I'm wondering how conditional probability relates to concepts of sample space, observation space, random variable, etc. Using the notation introduced in the OP here, how would one define the standard notation for conditional probability "P(B|A)" where A and B are both subsets of some sample...

The ABC manufacturing company purchases a certain part from two suppliers (A supplier & B supplier). The parts received from the suppliers are used to produce the company’s major product. The parts received from the suppliers are either defective or good parts. The A supplier provides 80% of all...

Hi friends, The problem: Assume the events A_i for i=1,2,...,n are of the same type. please trace the following relations. P(X│A_1 A_2…A_n )= \frac{P(X)}{P(A_1 A_2…A_n )} P(A_1 A_2…A_n│X)= \frac{P(X)}{P(A_1 A_2…A_n )}[ (-1)^{n-1} P(⋃_{i=1}^{n} A_i │X)+(-1)^{n-2} {n \choose 1}...

Hi everyone, The problem: Is this relation true? If so, how (or maybe where) it could be proved?P(A│B∪C)≤P(A│B)+P(A│C)-P(A|BC) and what about its possible generalization? thanks a lot in advance.

Hello, I'm hoping I'm asking this in the right place. If not, I apologize. Anyway, I have a dilemma about some basics in probabilty and pattern recognition, and, hopefully, someone can help me. I'm not sure I understand what class-conditional pdf f(x|w_{i}) really means, and it's...

For an exponential random variable X with rate u What is E{X|X>a} where a is a scale value from searching in internet I found that E{X|X>a}=a+E{x} but I can not prove it Help please

Homework Statement For an exponential random variable X with rate u What is E{X|X>a} where a is a scale value Homework Equations The Attempt at a Solution

Absolute Convergence, Conditional Convergence or divergence... Homework Statement \sum_{n=1}^{\infty} \frac {(-2)^{n}}{n^{n}} Homework Equations \lim_{n \rightarrow \infty} | \frac {a_{n+1}}{a_n}| < 1 \;\; absolute\; convergence \lim_{n \rightarrow \infty} | \frac...

The discrete random variable X has probability density P(X=x) =kp^x for x=0,1,... where p \in (0,1). Find normalizing constant k and E(X) as functions of p. For each integer x>0 find P(X>=x) and hence find P(X=y|X>=x) for each integer y>0. found k=1-p E(X)=\sum kxp^x =p/(1-p) P(X>=x) =...

Homework Statement A car dealer estimates that 50% of customers entering the dealership will buy a normal car, 20% will buy a high-end car, and 30% are just browsing. If 5 customers enter his dealership on a particular day, what is the probability that two will purchase high-end models, one...

I am attempting to do a simple volume integral over a particular shape. However Mathematica will not simply return an answer. For my input Volume = Integrate[ Integrate[Integrate[1, {z, 0, c}], {y, 0, b}], {x, 0, a}] + Integrate[ Integrate[Integrate[1, {z, c, c + a}], {y, b/2, b...

How can I find the conditional probability density function of a dependent variable given the independent variable set. Say, Y is some deterministic function of a set of variables X , or Y=f(X)+e. How can I fine the conditional pdf or P(Y|X) ?

How would I evaluate the following: P(A|(B or C)) where B and C are two mutually exclusive events. I have scoured a couple texts and the internet but have made no headway, any insight would be greatly appreciated. QN

"Every student in this class has studied calculus". Q(x): x is in this class. P(x): x has studied calculus. How come we have Q(x)->P(x) but not Q(x) ^ P(x)? What really is the difference?

This is part of the study guide for an exam and I'm not sure how to start. Homework Statement Consider three identical-looking dice. Two of the dice are ordinary fair dice (six equally-likely faces, numbered 1,2,...,6), but the third die is "loaded" (the face that ordinarily has a 1 has...

I have a long C++ program that has a few simple statements in it. At the beginning I have ; #define NUM_DP 10 Further on in the program I have this conditional statement; short int ct, j; . . . ct = op2.test(op2.num); if (ct < (NUM_DP - 1)) for (j = 1; j < 20...

Hello, I need help constructing a drop-down menu in Mathematica with options depending on the selection from a previous drop-down menu. The example is first the user selects a continent, and then the second drop-down menu shows the respective countries. Any help would be much appreciated.

Consider this scenario: "From families with three children, a family is selected at random and found to have a boy. What is the probability that the boy has an older brother and a younger sister? Assume that in a three-child family all gender distributions have equal probabilities."...