Create an example for (a) poisson distribution and (b) gamma distribution. Then, for both examples, compute an exact probability AND the normal approximation.

Q: In an insurance company the number of claims are modelled as a Poisson process with rate > 0. Assume…

A: Number of claims are modelled as a Poisson process with rate .Premium income per unit time = Let…

Q: 1. Continuous random variables 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2 have joint probability density function…

A: The Joint PDF of X and Y  is :f(x,y)=3x2+4y320≤x≤2,0≤y≤2

Q: ● O The prior probabilities for events A1 and A2 are P(A1) = 0.30 and P(A2) = 0.60. It is also known…

A: The prior probabilities for events  and  are,

Q: represented by a scalar x with Gaussian class-conditional probability density functions (pdf) p(x |…

A:

Q: For the following exercise, a fair coin is tossed 4 times, with the results noted each after each…

A: We have given that a fair coin is tossed  times.

Q: Q5 The weights of bags of Cements produced by Oman Cement Company are normally distributed with mean…

A:

Q: 7. The simplest type of inheritance occurs when a trait is governed by a pair of genes, each of…

A: Let the steady state matrix be .

Q: Find the value of the probability of the standard normal variable Z corresponding to this area: P(Z…

A: From the information, given thatLet Z denotes the standard normal variable with a mean of 0 and the…

Q: In a survey of 327 people, the following data were obtained relating gender to political…

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

Q: For the following exercise, a fair coin is tossed 4 times, with the results noted each after each…

A: The objective of this question is to find the probability of getting the same number of heads and…

Q: Suppose repetitions are not allowed. Randomly pick up a three-digit number that is formed from the…

A: The objective of this question is to find the probability that a randomly picked three-digit number,…

Q: A university is putting together a hiring committee of 6 members for the next university provost.…

A: We have given information,We have formed a committee of  members, and The members who are eligible…

Q: It is certain that a lacrosse goalie will successfully make a save 91.83% of the time. Suppose that…

A: The probability that a lacrosse goalie will successfully make a save of the time is 0.9183.A sample…

Q: How many positive integers with 6 or less digits are odd or divisible by 5 and do not contain any…

A: The provided information is as follows:The objective of the given example is to find the total…

Q: Q3. Approximately 20% of cars have been recalled for a manufacturer's defects but have not repaired.…

A: From the provided information,

Q: (4xy, 0<x,y< 1, f(x, y) = (o, elsewhere.

A: We have given a joint probability density function of random variables X &amp; Y as…

Q: Which of the following is NOT a valid probability density function? 0.04x for 0<x<5

A: Condition for valid density function:

Q: C1. A collector wants to collect football stickers to fill an album. There are n unique stickers to…

A: A collector wants to feel a football sticker album, and there are  unique stickers to collect. Each…

Q: A bag of M&Ms contains 7 blue, 3 brown, 5 orange, 3 yellow, 4 red, and 5 green. Reaching into the…

A: It is given that a bag of M&amp;Ms contains Blue = 7Brown = 3Orange = 5Yellow = 3Red = 4Green =…

Q: Old MathJax webview X = cos (0) (₪, 0 ≤ 0₁ < 0₂ < π) Draw the probability density function of the…

A: The cosine function decreases monotonically from 1 to -1 as  goes from  . Therefore, for in the…

Q: 23 In Exercise 6.1, we considered a random variable Y with probability density function given by…

A: The pdf of the random variable Y is given a. U1=2Y+1b. U2=1−2Yc. U3=Y2

Q: Complete the following table (fill in the missing probability distributions and calculate the joint…

A: An incomplete probability distribution table is givenLife yearsSalvage ValueJoint Probability…

Q: o that solution.  (a)  ∫ (15x^8)(e^(-x/4) (bounds: 0 to infinity) (b)  ∫ (10x^3)(1-x)^7 (bounds: 0…

A: a.∫15x8e(−x/4)0 to infinity limit b.∫10x3(1−x)70 to 1 limit

Q: 5. Suppose we have an M/M/2/4 queue with average service time of 6 minutes, and we have found the…

A: The given information is as follows:The stationary probablities are The average service time is…

Q: 5. The random variable Z is defined to be the sum of two independent random vari- ables, X+Y. The…

A: To determine the probability density function (PDF) of the random variable Z = X + Y, where X has an…

Q: In an insurance company the number of claims are modelled as a Poisson process with rate X > 0.…

A: Number of claims are modelled as a Poisson process with rate .Premium income per unit time = Let…

Q: Using the regression with the values rounded to the nearest hundredth, find the value of y at x = 9.…

A: From the provided information,…

Q: An experiment using samples from the same random variable as described in ques- tion 7 will be…

A: Given thatConsider,

Q: 14) For his birthday party, Madonna's 3 students bought him a cake cut into 10 slices. a) How many…

A: Given that for the birthday party, Madonna's 3 students bought him a cake cut into 10 slices.

Q: Select the correct choice below and, if necessary, fill in the answer box to complete your choice.…

A: It is given that the sample size is 63 and population standard deviation σ is unknown.

Q: 4. Determine the expected value and variance of the random variable whose PDF given by¹ where A is a…

A: Let X has a pdf

Q: Two independent random variables are defined with the following distributions: X 1 2 3 (a) Р 0.5 0.2…

A: It is given that  and  are two independent random variables with probability distribution…

Q: Inventing the exam. There is a fifteen-question probability test, according to your math professor.…

A: The provided information is as follows:The total number of questions in the probability test is…

Q: 8. x -3 -1 1 3 5 P(X = x) 0.17 0.28 0.15 0.27 0.13

A: We have given the probability mass function of a random variable  as follows:…

Q: How many different birth orders with respect to gender are possible in a family with six children…

A: Solution-:We want to find out how many different birth orders with respect to gender are possible in…

Q: 3x² + 4y 32 (a) Find and simplify a formula for the marginal density function fx(x). (b) Compute…

A: Let X and Y have joint pdf s

Q: In a random survey of students concerning student activities, 30 engineering majors, 23 business…

A:

Q: 1. Xt125 solve for P(-0.5 ≤X ≤ 1.5) 2. XX solve for P(X ≤ 1) 3. X F10,125 solve for P(X2 2.519) 4.…

A: 1)The t distribution with degrees of freedom 125.2)Distribution: Chi-square with 1 df3)F…

Q: 4. Estimate the probability distribution for rolling three 6-sided dice and taking their sum y = x₁…

A: Three six-sided dice are thrown and their sum is taken.be the number on the upper face of die.…

Q: A food safety guideline is that the mercury in fish should be below 1 part per million (ppm). Listed…

A: Here, there are 7 sample observations.The sample mean is computed as follows:The sample standard…

Q: Suppose 16​%of the population are 63 or​ over, 28​% of those 63 or over have  loans, and 54​% of…

A: Let's denote the events by using letters:A is the event that a person is 63 or overB is the event…

Q: People often decide their outdoor activities according to the weather conditions. Suppose you have a…

A: Given:3 weather states: W=(w1, w2, w3)3 Activity options: V=(v1, v2, v3)Initial state probabilities:…

Q: A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without…

A: We have given a box that contains one yellow, two red, and three green balls.We have to choose two…

Q: Problem 5 Let N₁ (t) and N₂ (t) be two independent Poisson processes with rate ₁ and >₂…

A: To show that given we can use the properties of Poisson processes.Let's define some variables:N1(t)…

Q: 2. The random variable z describes the observation of a physical phenomenon whose statistical…

A: The statistical problem involves the observation of physical phenomena described by random variable…

Q: Find the critical values x² = x₁-a/2 and XR 2 = 13. 95% degree of confidence and the sample size n…

A:

Q: The odds against chip beating his friend in a round of golf are 3:1. Find the probability that chip…

A: The objective of this question is to find the probability of Chip beating his friend in a round of…

Q: X is a normal random variable with mean 20 and standard deviation 50. Find the probability that 15 <…

A: Given,The mean = μ  =20The standard deviation = σ =50By using the standard normal distribution, [z].

Q: A fun size bag of M&Ms has about 17 candies. You open one of the bags and discover: 3 Blues, 4…

A: From the information, given thatThe total number of candies=17The total number of blue candies =…

Q: The score for freshmen on an aptitude test at WSU Vancouver has mean of 560, with a standard…

A: The provided information is as follows:The   is a random variable having mean ..The standard…