Problem #5: Suppose that X and Y have the following joint probability density function. f(x, y) = y₁ 0 < x < 7, y > 0, x −4 < y < x +4 620, (a) Find E(XY). (b) Find the covariance between X and Y.
Q: Let X be a continuous random variable whose probability density function is given by the formula if…
A: To find the probability that X is between 3 and 7, we need to calculate the definite integral of the…
Q: It is assumed that the results of a test follow a normal distribution with a mean of 78 and a…
A: It is given that the mean is 78 and the standard deviation is 6.
Q: A bag contains 3 red marbles, 5 blue marbles and 4 green marbles. If three marbles are drawn out of…
A: Given that, Number of red marbles = 3 Number of blue marbles = 5 Number of green marbles…
Q: The significance level alpha (a) is needed to identify the O population standard deviation Otest…
A: The study is about the significance level apha.
Q: The default a level generally accepted as the standard for social science research is 5
A: Asked for The default level generally accepted as the standard for social science research We know…
Q: 6. The weather forecaster says that tomorrow there is a 19% chance that it will rain. Which word or…
A: From given,Weather forecast says that there is a 19% chance.Probability of success is = 0.19
Q: via python. It’s the -number of accidents v hour of day -number of accidents v time period -…
A: Statistical testing is a powerful tool used in data analysis to draw meaningful conclusions and make…
Q: Problem #2: Suppose that two teams play a series of games that ends when one of them has won 3…
A: Probability of winning by team A is =1/5Two teams play a series of games end when one of them won 3…
Q: Problem 4: We are throwing darts at a disk (i.e. a filled in circle) shaped board of radius 5. We…
A: “Since you have posted multiple questions, we will provide the solution only to the first question…
Q: x)=1,2,..., 6. lculate the mean and variance of the number o library to a borrower. dom variable…
A: (a) To calculate the mean and variance of the number of books issued by the library to a borrower,…
Q: An article reported that for a sample of 56 kitchens with gas cooking appliances monitored during a…
A: The mean =654.16standard deviation =162.85The…
Q: athletes
A: The conditions for inference are not met in this scenario. Firstly, the athletes in the study were…
Q: Q1 (a) The data in Table Q1(a) shows the time or period in months starting from a hiring stage to a…
A: N = 25 Data : { 5,7,229,453,12,14,18,14,14,483,22,21,25,23,24,34,37,34,49,64,47,67,69,192,125 } We…
Q: The answer is incorrect
A: Answer Mean =110 Standard deviation =15
Q: In a class of students, the following data table summarizes the gender of the students and whether…
A: Since you have posted multiple questions, we will provide the solution only to the first question as…
Q: Q2 (a) Given there is a 0.90 probability that any UTHM's students subject. Using the binominal…
A: n=6, p=0.90X~Binomial(n=6, p=0.90)Let X be the number of students who scored E.p be the probability…
Q: solve using normal distribution rules x ~ n (25,5^2) find k such that p(20
A: Mean()=25Standard deviation()=5
Q: 76
A: To construct a table of values for the function f(x) = 0.905, starting at x = 0 and incrementing by…
Q: Assume a data set D is observed by three models M₁, M2, and M3 which all follow a normal…
A: We can use Bayesian inference and calculate the posterior probabilities based on the given prior…
Q: Problem #2: Suppose a random variable X has expected value E[X]=-2 and variance Var(X) = 4. Compute…
A: Suppose the random variable has,Expected value: and Variance:
Q: In how many ways can we arrange 9 rings on 4 fingers of the right hand (excluding the thumb), if:…
A: As per our guidelines we are supposed to answer only 3 sub-parts. a) In this scenario, we have 9…
Q: 1.En una urna hay 20 bolas, 10 de ellas son rojas y 10 son verdes. Se extraen al azar 5 bolas sin…
A: As per policy I have calculated first main question plz REPOST for remaining questions. Here given…
Q: Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa.…
A: Delta airline quotes a flight time of 2 hour and 5 minutes. actual flight times are uniformly…
Q: If X is uniform on [2, 6]. Find a. P(X > 3), b. P(4 ≤ x ≤ 5)
A: X~U(a,b) probability density function pdf of uniform distribution is. f(x)=1/(b-a) , a<x<b
Q: How many di erent arrangements are there of the letters A, B, C, D, E, and F for which E is not the…
A: Here total 6 letter are available. Letters are A , B , C , D, E, F .here use counting principle. n!…
Q: Suppose X has density function f(x) = cx(1-x) for 0 2.
A: The density function f(x)=cx(1-x) for 0<x<1 0 otherwise We…
Q: In a certain mathematics class, the probabilities have been empirically determined for various…
A: number absent0123456Probability0.020.040.20.230.310.10.1
Q: The following table represents the highest educational attainment of all adult residents in a…
A: total number of students=20966 total number of students with high school only=4550 total number of…
Q: The Central Limit Theorem tells you how to approximate certain distributions using the normal…
A: Sample size (n)=40 Probability of passing mark (success)(p)=0.5 (equally likely to occur as either…
Q: Use an Euler diagram to determine whether the argument is valid or invalid. No mathematics test is…
A: Euler diagram: It is a diagrammatic representation. It represents sets and their relationships.
Q: he probability distribution of a discrete random variable X is given. P(X=1/8)=? x -2 -1 0 1 2…
A:
Q: A random variable X has the following probability mass function defined in tabular form as shown…
A: x-112P(X=x)2c3c4c
Q: Continuous random variables X and Y have the following joint PDF: -1 ≤ x ≤ 1, 0≤ y ≤ x² In x², to,…
A: Let X and Y have a joint density function
Q: The table to the right shows four states, their 2010 populations, and their number of seats in a…
A: State Population SeatsA1179100012B1633200016C1070500010D1267500013
Q: Part: 3/4 Part 4 of 4 (d) Would it be unusual for 10 or more of the flights to be on time? Use a…
A: It is given that the observations are independent with probability of success p = 87% = 0.87 and…
Q: In hypothesis testing, why do we start with a no-difference null hypothesis and then try to reject…
A: A null hypothesis is a statement of no difference between the population parameter and a…
Q: In a recent poll of 300 home-owners in Calgary, 240 said that they would not vote for a particular…
A: AS per guidelines i have calculated 1st main question , plz repost for remaining . As first question…
Q: A particle executes an unrestricted simple random walk on the line with p=0.7 and q=0.3. Its…
A: To calculate the probabilities of the given events in the simple random walk, we need to use the…
Q: A six sided fair die is rolled in times. If you are concerned about the probability of five comes up…
A: Each roll of the dice may be considered as a Bernoulli Trial, that results in "success" if 5 comes…
Q: Problem 2: Suppose a random variable X has expected value E[X] = -2 and variance Var(X) = 4. Compute…
A: Note: As per our guidelines we are supposed to answer only question per post so i am solving first…
Q: a) What is the probability that a car is a Sedan given that it is white? b) What is the probability…
A: here define event ,S= car is sedan W = car is white in color p(S) = 0.30p(W) = 0.55p(W | S) = 0.22
Q: The aircraft for a particular flight has 72 seats. The airline's records show that historically for…
A: Number of passengers Probability of passengers who purchase a ticket and arrive to board the flight…
Q: What is the probability of rolling two fair six-sided dice and obtaining a sum of 7, given that the…
A:
Q: A bag contains 12 gambling chips: 8 of these chips have a zero marked on them, the other 4 chips…
A: Please note that as per our guidelines if multiple sub-parts are there in a question we can answer…
Q: Charlie Ticket Bus $1.50 $2.00 Subway $2.00 $2.50 Table 6.21. MBTA fare increases [R187] a. What are…
A: a. To calculate the relative change in the Charlie Card bus fare, we subtract the existing fare from…
Q: Suppose that an airline uses a seat width of 16.8 in. Assume men have hip breadths that are normally…
A: From the provided information, Mean (µ) = 14.7 Standard deviation (σ) = 0.9 X~N (14.7, 0.9)
Q: How many ways are there of arranging the 26 letters of the alphabet so that none of the words be,…
A:
Q: Suppose you roll 2 dice. What is the pobability that the sum of the 2 dice is s 7, given that the…
A:
Q: During the exam you will be using a sample of 500 adults with the following variables: genhelf -…
A: If the variable is categorical (non-numerical) and there is natural ordering in it, then the…
Q: A random variable follows the normal probability distribution with a mean of 100 and a standard…
A:
Please show a step-by-step solution. Do not skip steps, and explain your steps. Write it on paper, preferably. Make sure the work is clear.
Step by step
Solved in 4 steps with 4 images
- J 1 Problem 126. Let X and Y be discrete random variables with joint probability mass function pX,Y (x, y) = C/[(x + y − 1)(x + y)(x + y + 1)], x, y = 1, 2, 3, . . . Determine the marginal mass functions of X and YProblem 1. A continuous random variable X is defined by f(x)=(3+x)^2/16 -3 ≤ x ≤ -1 =(6-2x^2)/16 -1 ≤ x ≤ 1 =(3-x^2)/16 -1 ≤ x ≤ 3 a)Verify that f(x) is density. b)Find the MeanQuestion 1 : Suppose that the probability density function (p.d.f.) of the life (in weeks) of a certain part is f(x) = 3 x 2 (400)3 , 0 ≤ x < 400. (a) Compute the probability the a certain part will fail in less than 200 weeks. (b) Compute the mean lifetime of a part and the standard deviation of the lifetime of a part. (c) To decrease the probability in part (a), four independent parts are placed in parallel. So all must fail, if the system fails. Let Y = max{X1, X2, X3, X4} denote the lifetime of such a system, where Xi denotes the lifetime of the ith component. Show that fY (y) = 12 y 11 (400)12 , y > 0. Hint : First construct FY (y) = P(Y ≤ y), by noticing that {Y ≤ y} = {X1 ≤ y} ∩ {X2 ≤ y} ∩ {X3 ≤ y} ∩ {X4 ≤ y}. (d) Determine P(Y ≤ 200) and compare it to the answer in part (a)
- Problem 7: Let X be a continuous random variable with the probability density for f(x) = 3x2 values of x in [0,1], and f(x) = 0 elsewhere. Compute the expected value and variance of X.Problem#1: On the desk of an office of a Banking Company, the arrivals of the customers follow poisson law and an average at every 10 minutes a customer arrives. The officer responsible takes on an average 6 minutes to serve a customer, assuming the exponentially distributed. Find out the average arrival rates for(a) 1 hour(b) 15 minutes(c) 8 hoursRework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 12 markers: 9 that contain ink and 3 that do not contain ink. A sample of 6 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. Find the probability density function. Be certain to list the values of Y in ascending order.
- Question 3 Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will be equal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their income will be y − L. The chance of a safe return is 50%. Now suppose that there are two identical merchants, A and B, who are both risk averse expected utility maximisers with utility of income given by u(y) = ln y. The income of each merchant will be 8 if their own ship returns and 2 if it sinks. As previously, the probability of a safe return is 50% for each ship. However, with probability p ≤ 1/2 both ships will return safely. With the same probability p both will sink. Finally, with the remaining probability, only one ship will return safely. (iv) Compute the increase in the utility of each merchant that they could achieve from pooling their incomes (as a function of p). How does the benefit of pooling depend on the probability p? Explain intuitively why this…Problem 1. Consider the following density function. f(x )=[ (kx) ^ (2/3) * 0 < x < 2 Find the value of k. Find the cumulative distribution function ( CDF) of X Find the inverse of the CDF. Simulate a random sample of 10000 values from the above distribution by using inversetransformation and find the mean and the variance of those values, and write the Rcode.If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?
- What is the value of the constant c for p(x) to qualify as a probability mass function? ?(?)=?(1/4)x-1 ?? ? = 1, 2, 3, 4, 5, ... and p(x) = 0 otherwise. How would you get c{1-1/4}-1 = 1Question 1.2 Consider the function f (x) = (1/24(x^2 +1) 1 < or = x < or = 4) = (0 otherwise) Calculate P (x = 3) Calculate P (2 < or = x < or = 3) Question 1.3 Consider the function f (x) = (k - x/4 1 < or = x < or = 3) = (0 otherwise) which is being used as a probability density function for a continuous random variable x? a. Find the value of K b. Find P (x < or = 2.5)4 (b) An insurance company provides customers with both auto and home insurance policies. For a particular customer, Χ is the deduction on his or her auto policy and Y is the deduction on the home policy. Possible values of Χ are K100 and K250, and for Y are K0, K100 and K200. The joint probability density function for ( ) ,YΧ is given by the following table: Χ Y K100 K250 K0 0.20 0.05 K100 0.10 0.15 K200 0.20 0.30 iv. If we look only at those insurance customers selecting the lowest auto mobile insurance deduction (K100), what is the probability that a randomly selected\ customer will also select the lowest home deduction (K0). v. Compute the correlation coefficient of Χ and Y
