Find an example with two events, A and B, which are independent but not condi- tionally independent with respect to another event C. (b)  Find an example with two events, D and E, which are conditionally independent with respect to an event F but not with respect to Fc.

Q: Customer Andy Betty Cindy David Ellen Age 36 21 63 59 24 Income (k) 35 50 200 170 40 Frank 37 50 /ho…

A: We'll calculate distance of Frank from everyone else, using the Euclidean measure of distance.…

Q: 1. (a) (b) When a hand of 5 cards is dealt from a standard deck of 52 cards, what is the probability…

A: NOTE: Hi there! Thanks for posting the question. As per our guidelines, we will solve the first…

Q: Prove- Assume that X1 ∼ P oi(λ1), X2 ∼ P oi(λ2). Assume also that X1 and X2 are independent.…

A:

Q: Complete the following. (a) Calculate how many numbers between 100 and 699 contain exactly one 1 by…

A: Given: We need to calculate the numbers between 100 and 699 that contain exactly one 1 by…

Q: This problem involves a sample space S with two events, E and F. Assume that Pr[E]=8/15…

A:

Q: 9. Let p(x) = 4 T(1 + (2x)²) for 20 (and p(a) = 0 if a <0). (a) Show that p is a probability density…

A: 9. Given that p(x)=4π1+2x2 for x≥0.  First, we have to show that p is a probability density…

Q: 3.    A study found that there was a 48% chance that a driver fails a breathalyser test when it is…

A:

Q: You select 3 cards from a deck of 52 cards (without replacement). What is the probability that you…

A: select 3 cards from standard deck of 52 cards without replacement P(atleast one ace) = ?

Q: Suppose we want to choose 3 colors, without replacement, from the 4 colors red, blue, green, and…

A: 4 colours : {red,blue,green,purple}select 3 colours at random without replacement(A) no. of ways to…

Q: The circle graph represents a sample of 600 people who were asked which one automobile accessory…

A: A sample of 600 people were taken.

Q: A company receives 30% of its shipments from source A and the rest from source B. For source A, the…

A: Let S1 denotes the event that a randomly selected shipment is from source A and S2 denotes the event…

Q: Let X be a discrete random variable with the following PMF 0.5 for k=1 0.3 for k = 2 0.2 for k = 3 0…

A:

Q: 5. In a supermarket, the weights of apples and pears have approximately normal distributions. The…

A: Let X be the weights of apples follows normal distribution with mean 150 and standard deviation 15.…

Q: Question 1, 44 of my 55 neighbors don't like me. What is the probability that in a random sample of…

A: given data 44 of my 55 neighbour don't like me. select sample of 5. P(exacly 4 of selected 5 don't…

Q: A box has four cards numbered 1, 2, 3 and 4. Keiko will toss a coin once and record the toss as…

A: From given  A box has four cards numbered 1, 2, 3 and 4. And let H=Heads T=Tails

Q: ping pong ball is drawn at random from an urn consisting of balls numbered 4 through 12. A player…

A: Given From the numbers 4 to 12 5 of them (4,6, 8, 10, 12) are even numbers and remaining 4 of them…

Q: 11) According to a recent report, 68.3% of men and 64.1% of women in the US are overweight. Given…

A: Given: 68.3% of men are overweight. 64.1% of women are overweight. 49.3% of Americans are men 50.7%…

Q: (a) What is the break-even volume? units (b) What is the break-even revenue? (c) What are the…

A: see the attachment.

Q: Q2) The jpdf of X and Y is fxy defined as: Z = X +Y. Find the pdf fz(z). (x,y)==-[u(y)-u(y-2)]…

A:

Q: Phyllis invested 42000 dollars, a portion earning a simple interest rate of 4 percent per year and…

A: According to the information provided in the question,  Amount Phyllis invested = $ 42000 Earning…

Q: Prove - If X and Y are independent random variables, then E(XY ) = E(X)E(Y ). (You can assume that…

A: Assume that X and Y are two independent discrete random variables.

Q: Rafael is at the grand opening celebration of a supermarket. He spins a wheel with 10 equal-sized…

A:

Q: 10. Suppose {Xn, n ≥ 1} are independent random variables. Show P[sup Xn M] < 0o, for some M. n

A: Given::-

Q: Of 100 students, 26 can speak French F, 33 can speak German G, and 16 can speak both French and…

A: Given that  Total students = 100 Speak French= F = 26 , Speak German = G =33 , Both Speak French and…

Q: 9) You are given the following data regarding the probabilities of two events E and F: P(EUF) = 0.8,…

A: For any two events A and B, union of A and B, is the occurrence of either A or B or both. In other…

Q: 2. For the rug below, decide which color you would predict as most likely to be hit. For each color,…

A:

Q: A ball is drawn from a bag containing 8 red balls numbered 1-8 and 7 white balls numbered 9-15. What…

A: It is given that  No. of red balls = 8    ( from 1 to 8 ) No. of white balls = 7    ( from 9 to 15 )…

Q: A supermarket wants to send codes for $0.25 off a bag of chips to its rewards program members. Each…

A: code have one digit followed by four letters. letters D and E and digits 0,5 and 8 will not used.so…

Q: The ice cream shop has 7 types of toppings available, and you decide to add 4 toppings to your bowl…

A: Given information- We have given that the ice cream shop has 7 types of toppings available. So, n =…

Q: Raina is playing a carnival game. She is blindfolded while she throws a dart at a board of 12…

A: From given we have : S = 1 M = 8 L = 2 XL = 1  total 12 balloons

Q: 2.2 In each of the following find the pdf of Y. (a) Y = X² and ƒx(x) = 1, 0 < x < 1

A:

Q: Question 2. Normal Distributions [ 1 It is known that the average time spent by a tourist at Eiffel…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: Deandre has a salary of $82,100. What are his gross semi-monthly earnings?

A: Semi monthly earning is calculated using the annual salary. In semi average method, the time period…

Q: A bag contains 3 nickels, 5 dimes, and 4 quarters. If you draw 3 coins at random from the bag,…

A: It is given that  Nickels coins = 3 Dimes coins = 5 Quarters coins = 4 Total coins = 12

Q: What is the probability all nine shark attacks are nonfatal? (Round your answer to three decimal…

A: Given that  n = 9 , p = 55% = 0.55 , q = 1 - p = 1 - 0.55 = 0.45 R ~ Binomial (n = 9 , p = 0.55) R :…

Q: 6. In a college, 400 students are graduating this semester. According to the school policy, each…

A: 6) Let X denotes the number of people a student will bring to the graduation ceremony. Based on the…

Q: As part of a research project, the blood pressures of 2000 patients in a hospital are recorded. The…

A: given data, normal distributionμ=125σ=13we have to find out the percentile for the normal…

Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A: given data, each license plate in a certain state has four letters followed by two digitthe…

Q: 12) There are two boxes, A and B. Box A contains 4 blue balls and 6 red balls, while box B contains…

A: 12) It is given that the probability of choosing box A is 13.

Q: An audio equipment store has nine different amplifiers, five tuners, six turntables, eight tape…

A: 9 amplifiers5 tuners6 turntables8 tape decks7 compact disc players12 speakersall components are…

Q: If you are dealt 5 cards from a shuffled deck of 52 cards, find the probability that all 5 cards are…

A: We have given that Total number of cards = 52 We have to draw five cards

Q: 1. (a) When a hand of 5 cards is dealt from a standard deck of 52 cards, what is the probability…

A: Probability is the chance that an event happening. It is also known as likelihood of the event…

Q: raffle is going to be held in which there is a first prize worth $400, and a second prize worth…

A: given data, first prize worth $400secound prize  worth $100n=100fair price for a ticket =?

Q: : December 15, 2022 at 10:28 AM A t test was carried out to determine if the number of words that a…

A: Given that  Sample size n =24 Sample mean=78 Standard deviation =3

Q: Solve the problem by applying the Fundamental Counting Principle. A restaurant offers a choice of 4…

A: It is given that a restaurant offers a choice of 4 salads, 5 main courses and 4 desserts.

Q: If two fair dice are rolled, find the probability that the sum of the dice is 5, given that the sum…

A: Roll two fair dice  For rolling single dice outcomes possible are : {1,2,3,4,5,6} Total possible…

Q: Joyce paid $35.00 for an item at the store that was 30 percent off the origina What was the original…

A: Joyce paid $35.00 for an item at the store that was 30% 0ff the original price Then to find original…

Q: A bag contains 11 red balls and 13 white balls. Two balls are drawn without replacement. What is the…

A: Given that  Red balls = 11 , White balls = 13 Total balls = 11+13 = 24 2 balls are selected at…

Q: A9. Let X and Y be independent standard normally distributed N(0, 1) random variables. What is…

A: Given that  X and Y are independent standard normal distribution N(0 , 1).

Q: 0.9 0.4 0.4 0.1 0.2 to be ap L 2 3 5 6 0.2 0.6 0.7 1 0.3 0.2

A: we know that, In recurrent state, probability of returning to that state is one. Here, we can see…