Let A and B be events in a sample space S such that P(A) = 0.38, P(B) = 0.42 and P(An B) = 0.20. Find P(A | B). O 0.2500 O 0.4762 O 0.9048 O 0.0238 O 0.5263

Q: A total of 36 members of a club play tennis, 28 play squash, and 18 play badminton. Furthermore, 22…

A: A for tennisB for squashC for badmintonn(A) =36n(B) =28n(C) =18

Q: 3.1 Repeat observing a distance for n times with independent equal weight. Please proof that the…

A: To prove that the most probable value (MPV) of the observations is the direct mean by the Least…

Q: estaurant in Ohio, the number of minutes that diners spend at the table has a major impact on the…

A: X~N( μ , ?)μ=89 , ?=17Z-score =( x - μ )/?

Q: Assume the random variable x is normally distributed with mean μ = 85 and standard deviation o=5.…

A: The population mean is 85 and the population standard deviation is .

Q: usiness organization needs to make up a 8 member fund-raising committee. The organization has 6…

A: We have given that a business organization has 6 accounting majors and 6 finance majors and the…

Q: Given two dependent random samples with the following results: Population 1 48 29 32 29 38 31 28…

A: The formula for the Confidence interval for paired differences between the mean is:

Q: Suppose X and Y have joint probability density function 1/2 if 0 < x < 1, 0 < y < 1, 1/3 if 1<x<0, 0…

A: The joint density function of X and Y is,

Q: a.Here is the Markov Chain, then : Which state is communicating? Which are the transient states? The…

A: Given the transition diagram of the Markov chain:

Q: A fair coin is tossed 27 times. What is the probability that at most 24 heads occur? A) 0.99999718…

A: From the provided information,

Q: Can you help please: Suppose that X ∼ Geom(p). In chapter 2, we computed the CDF of X as FX(x) = 1…

A:

Q: A fair coin is tossed 17 times. What is the probability of getting exactly 14 tails?

A: A fair coin is tossed 17 times. The objective is to find the probability of getting exactly 14…

Q: In a lottery game a single ball is drawn at random from a container that contains 25 identical balls…

A: Container contain 1 to 25 numbered identical balls

Q: Consider two continuous random variables Y and Z, and a random variable X that is equal to Y with…

A: To find the PDF of random variable X, you can express X as a mixture of the PDFs of Y and Z.

Q: how many ways can a Math team of 9 students be chosen from a Math Club which consists of 14 seniors…

A:

Q: Let X be a Gaussian random vector with distribution [5 4 ~~ (B]. []). 5 X~N Let Ỹ be a Gaussian…

A: Given:Mean vector of X is:

Q: General Electric models the time X in years that a new microwave will last using the following PDF…

A: Given that X is the time in years that a new microwave will last. And its pdf is:f(x)=…

Q: Which of following z-scores (to the nearest two decimal places) has 75% of the area in the standard…

A: The area of z score for between -z to z

Q: Q4: Two cards are drawn from an ordinary 52-card deck without replacement. Given that one of the two…

A: The objective of this question is to find the probability that the first card drawn was a heart,…

Q: Vehicle speed on a particular bridge in China can be modeled as normally distributed. USE SALT (a)…

A: Let X denote the vehicle speed on a particular bridge in China &amp; X follows the normal…

Q: D. The Swiss embassy has 65 employees. Of these employees, 47 speak German, 35 Speak Italian, and 20…

A: Given,Total employees = 65Number of employees speak German, n(G) = 47Number of employees speak…

Q: List the complement of each set A, for the given Universal set, S. a) S-the set of whole numbers…

A: Given thata) Universal set (S) = The set of whole numbers less than 25S = {…

Q: 1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs…

A: Let the states of the given Markov chain areState 1: Running smoothlyState 2: Running but needs…

Q: Use the data given in the table below to compute the probability that a randomly chosen voter from…

A: From the information, given that

Q: Consider the following Venn Diagram, depicting the data from a survey of random customers who…

A: The given Venn diagram depicts the data from a survey of random customers who visited a local small…

Q: Suppose a continuous random variable X~Fx(x): f(x,y) = { 1/4e^-1x/4, if x≥0    0, x<0 } What is…

A: Given a continuous random variable :

Q: (a) Use this equation to derive a more general expression for a 100(1-a) % CI for μ of which the…

A: Given,Let 0,\alpha_{2}&gt;0 \)" data-mce-style="cursor: default;"&gt;α1&gt;0,α2&gt;0  with α1+α2=α…

Q: A voltage reference is an electronic device intended to output a constant voltage However, such…

A: A voltage reference is an electronic device intended to output a constant voltage.However, such…

Q: what the requirements are to assume that the sampling distribution of sample means does have a…

A: The objective of this question is to understand the conditions under which we can assume that the…

Q: 4) Environmentalists worry that the overconsumption of plastics may lead to catastrophic…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Consider two continuous random variables Y and Z, and a random variable X that is equal to Y with…

A: Y and Z are two continuous independent random variables and X is a random variable defined as:

Q: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.6…

A:

Q: What percent of the total population of data values are included at +/- 1 sigma? +/- 2 sigma? +/- 3…

A: What percent of the total population of data values are included at +/- 1 sigma? +/- 2 sigma? +/- 3…

Q: Here is a random variable and its PMF. Value of Xx=1 x=2 x=3 |x=4 x=5 x=6 Probability, P(X=x) Find…

A: The random variable  has its PMF given as follows: Value of 1234560.150.050.400.100.100.20

Q: Books from Sellsevere Press average 1 misprint every 4 pages. A new book coming out soon will have…

A: A Poisson distribution is defined as a discrete frequency distribution that gives the probability of…

Q: Two random variables X and Y with a joint PDF f(x,y) = Bx+y for 0≤ x ≤6 , 0≤ x ≤7 and constant B…

A: Given, the joint PDF of X and Y is

Q: roblem #6: Each day, John performs the following experiment. He flips a fair coin repeatedly until…

A: John flips a coin until he gets a T and counts the number of coin flips needed.

Q: and P(EF)=0.41. Find the following:

A: P(E)=0.73 ,P(F)=0.57 and P(E ∩ F)=0.41

Q: A large stockpile of used pumps contains 20% that need repair. A repairman is sent to the stockpile…

A:

Q: In a group of 112 students, 65 play football, 45 play hockey, 42 play cricket, 20 play football and…

A:

Q: Consider the following cumulative distribution function for the discrete random variable W. W 2

A: Given that  w1234P(W&lt;=w)0.30.440.721

Q: 2. Let X be a continuous random variable with probability density function (pdf) [3x² 0<x<1…

A: f(x)=3x2.       0&lt;x&lt;1 0.               OtherwiseWe have to find the probability density…

Q: Suppose that a student rolls two balanced dice three times in a row. What is the probability that on…

A: There are 6 number on each die so the total number of outcomes=6×6=36

Q: Suppose X and Y have joint probability density function [C(x²+y²), _if0<x<y<1, otherwise. f(x, y) =…

A: The formula to calculate the expected value of x is,The formula to calculate variance of x is,

Q: Suppose X and Y have joint probability density function C(x² + y²), if 0<x<y < 1, otherwise. f(x, y)…

A: Given, the joint density function of X and Y is

Q: Eighteen people decide to play softball. In how many ways can the 18 people be divided into 2 teams…

A: There are 18 people available to be divided into 2 teams.We want to create two teams with 9 people…

Q: Let X₁, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix 1/2 1/2 0 0 1/7 0…

A: We are given a transition probability matrix and state space of a Markov chain and asked to find its…

Q: 2- a) Find the value of k for which this is a valid joint PDF for the random variables X and Y. f(x,…

A: The joint PDF of X and Y is:f(x,y)=k(x2+y2)0≤x≤1 and 0≤y≤1Objective : a) Find Kb) Marginal…

Q: Candidate A and Candidate B have a hotly contested race for Florida's electoral votes. Suppose each…

A: P=0.5003We have 8084000 voters in Florida

Q: Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix (1/2 1/2 0 0 1/7…

A: We are given a transition matrix and state space of a Markov chain and asked to find the limiting…

Q: Consider two numbers X and Y picked independently with the following pdfs: (2x, 0≤x≤1 0, otherwise…

A: