Cars arrive at a toll booth according to a Poisson process at a mean rate of 15 cars every 30 minutes. Find the probability that the toll collector will have to wait longer than 28.41 minutes before collecting the 10th toll. Use two approaches to answer the question, namely (i) the relationship between gamma and Chi-square distributions, and (ii) the relationship between Poisson and gamma distributions. You can use R to obtain the final numerical answers.

Q: Create a tree diagram for the sample space of this experiment, if you toss a coin 4 times.

A: Here we have to Create a tree diagram for the sample space of this experiment, if we toss a coin 4…

Q: Construct a frequency table using a class interval width of 0.2 starting at 0.15. Type integers or…

A: Class interval 0.15-0.35 0.35-0.55 0.55-0.75 0.75-0.95 0.95-1.15 1.15-1.35 1.35-1.55…

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A: Answer: From the given data, Mean (μ) = 500 Standard deviation (σ) = 102 X follows normal…

Q: (a Find the moment-generating function of X 2 Geom(p).

A:

Q: 3. Let X be a discrete random variable with probability mass function p(n) = 7 (1)", Find the…

A:

Q: thinkco needs to hire 2 marketing research employees. how many ways are there for the company to…

A: Number of marketing research employees r = 2  Number of qualified applicants(n) = 10

Q: On a standardized exam, the score are normally distributed with a mean of 300 and a standard…

A: X~N( μ , ?)   μ=300 , ?=25   Z-score =( x - μ )/?

Q: Problem #8: (Urn Poker) An urn contains 11 red balls numbered 1 through 11, 11 yellow balls numbered…

A: To find the probabilities of getting specific hands in this poker-like game, we need to calculate…

Q: Tom, John, Fred, and Bill are friends whose occupations are (in no particular order) nurse,…

A:

Q: 2 The table shows the numbers of bags of different flavors of potato chips on a store shelf. A…

A: The number of bags of different flavors of potato chips on a store shelf is given below, Flavor…

Q: Poker Calculate the probability of being dealt the following poker hand. (Recall that a poker player…

A: It is required to find the probability of choosing a three of a kind poker hand, that is, a hand…

Q: Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing…

A: The bag contain three red marbles, two green ones, four white ones and two purple ones. She grabs…

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A: As per our guidelines we are supposed to answer only 3 sub-parts. a) The type I error is the…

Q: 4. An engineering construction firm is currently working on power plants at three different. sites.…

A:

Q: Suppose events E and F and mutually exclusive, with P (F) = 0.48 and P(E U F) = 0.56. Calculate the…

A: Here Given  events E and F and mutually exclusive, with P (F) = 0.48 and P(E U F) = 0.56.

Q: Is the probability of a bowler rolling a strike higher after he has thrown four consecutive strikes?…

A: Bowler After Four strikes After Four Non-strikes 1 0.632 0.421 2 0.684 0.4 3 0.61 0.529…

Q: If n= 9 the equation is incorrect, hence, the answer is wrong. Please revise.

A: To determine the sample standard deviation, you will need to have a set of sample data. Once you…

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A: probability of spending $700 or more on gaming before leaving town(p)=0.72 sample size(n)=2 Let "x"…

Q: 4. Suppose that the probability density function of X is f(x) = {3x² 0<x< 1 0 elsewhere Determine P…

A: The required probability is,

Q: Use the counting techniques from the last chapter. A bag contains two red marbles, three green ones,…

A: Number of red balls = 2 Number of green balls = 3 Number of fluorescent pink = 1 Number of yellow…

Q: A committee is to consist of a chair, two hagglers, and three do-nothings. The committee is formed…

A: A committee is to consist of chair , two hagglers and three do nothings. The committee is formed by…

Q: Fill in the blanks using the named events. A? 30% of all lawyers who lost clients (L) were antitrust…

A: We have given that, 30% of all lawyers who lost clients L were antitrust lawyers A, whereas 10% of…

Q: 46 15 a. b. er the data set be C. d. 44 57 49 31 53 48 57 14 You must show your work to earn full…

A: Data 46 44 49 53 57 20 104 42 15 57 31 48 14 71 24 56

Q: Since an instant replay system for tennis was introduced at a major tournament, men challenged 1402…

A: Here from Given Information n1 =1402n2 =744X1 = 430 X2 = 212p1^=4301402 = 0.31p2^=212744 = 0.28

Q: The amount of time that people spend going through airport security at a busy airport is normally…

A: Mean(μ)=25 standard deviation(σ)=4.8

Q: Question 2 Let X be an exponential random variable with probability density function px(x) = }e-f…

A: Probability density function of X is p(x)=(1/3)×e-(1/3) , x≥0

Q: Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard…

A: The random variable X is the IQ score of adults It is normally distributed. The mean is 100. The…

Q: Two unbalanced dice are thrown at the same time. The first die has the property that the probability…

A: a. The probability of getting a 1 or a 6 on the first die is three times the probability of getting…

Q: X is a continuous random variable and its density function is Jkx ƒ₂(x) = { {0 What is k? O a. 1 O…

A: Given the pdf. of a continuous random variable f(x) = kx0≤x≤10otherwise What is k?

Q: Outcome Probability What is the probability of rolling less than 4? HINT [See Example 3.] 3 5 6

A:

Q: A system of electronic tubes is connected as in Figure 1. The time to failure of each component…

A:

Q: Problem 4. Let X = (X₁, X2,..., Xn) be i.i.d. where each X, has proba- bility mass function P(X = )…

A: a. To find the maximum likelihood estimator (MLE) of theta, we need to maximize the likelihood…

Q: a Airlines quotes a flight time of 6 hours, 15 minutes for its flight from Los Angeles (LAX), USA to…

A:

Q: 2. Prove Chebyshev's Inequality: Let X be a random variable with mean and variance o². Then for any…

A: First we define the variance definition Var(X)=E[(X-μ)2] expanding the above equation…

Q: 3. 11th and 12th grade students at Fairlawn High S The results of the survey are recorded in the…

A: From the given table:- Total no. of 11th  graded students = 8+32= 40 Total no.of 12th graded…

Q: Airlines for America (A4A) report that a family of four planning to travel over the holiday break…

A: Solution:- From given information Mean μ=3500 Standard deviation  σ=750 Assume that the amount spent…

Q: When Natalie commutes to work, the amount of time it takes her to arrive is normally distributed…

A: Answer:- Given, Mean, µ = 25  Standard deviation, σ = 4  Let X be a random variable represents the…

Q: Let (Nt)t>0 be a Poisson process with parameter λ=2. Find the following: (c) E(S3S4)

A: Let Nt be a Poisson process with rate parameter λ=2. The waiting times between successive events of…

Q: Suppose we want to choose 6 letters, without replacement, from 8 distinct letters. (a) How many…

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Q: wrong answer for letter c, it was asking the LOWER quartile.

A: Percent of calories consume by Americans follow normal distribution with mean 36  and standard…

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A: A shipment of 1000 sacks of oranges arrives at a distribution centre in Edinburgh, one of 10 such…

Q: You flip a fair coin 4 times. What is the probability that exactly two of those land on Heads? 1/2…

A: Number of trials n=4 Probability of head p=1/2

Q: Part 1: The Goodness-of-fit test The problems in this section are taken directly from the course…

A: The null and alternative hypotheses can be written as follows: Null hypothesis (H₀): The actual…

Q: Listed below are numbers of Internet users per 100 people and numbers of scientific award winners…

A: To construct a scatterplot, we plot the points (80.6, 5.3), (79.5, 8.9), (57.5, 3.4), (67.0, 1.7),…

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A: The information provided in the question are as follows :- There are 50 different numbers from 0 to…

Q: Compute the indicated quantity. P(B) = = P(A/B) = 0.4, P(AB) = 0.3. Find P(B).

A: P(A|B) = 0.4, P(A ∩ B) = 0.3 then,  We will find P(B) = ?

Q: 5. If you draw two cards from a standard deck of 52 cards without replacement, find: a. P(King…

A: Two cards are drawn from a standard deck of 52 cards, without replacement.

Q: No Commute 0-1 Hr Commute >1 Hr Commute Sum Restaurant 3 10 28 41 Take Out Home Cooked 10 18 22 50…

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A: Given that Two dice are rolled and number add to 10

Q: Let X ~ Hypergeometric (4, 3, 4). The random experiment defining X can be described as follows: from…

A: From the given information, X follows hypergeometric distribution. Here, 4 marbles are to be drawn…