If x and y are independent Poisson variable, show that the conditional distribution of x given x + y is binomial.

Q: The random variable X can only take the values ​​1, 2, 3 and 4 with equal probability. Determine the…

A: Given information: A random variable X has been given that can take only values 1, 2, 3 and 4. The…

Q: When do you call two random processes to be joiniiy wide-sense stationary ?

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Q: The number of patients who are received per hour in the emergency room of a hospital is a random…

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Q: If the number of users entering a metaverse is a Poisson random variable whose mean is 2 person per…

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Q: The deals cracked by an agent per day is a random Poisson variable with mean 2. Given that each day…

A: Probability distributions are of 2 types, discrete and continuous. Poisson distribution is a…

Q: Derive an interative  formula for the probability function of poisson distribution.

A: The binomial distribution works when we have a fixed number of events n, each with a constant…

Q: If 40% of all commuters ride to wirk in carpools, find the probability that if 8 workers are…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If Y Poisson(2) and Z Poisson(3) are independent, what is distribution of W = Y + Z?

A: Solution: Given  Y~Poisson(2)    and  Z~Poisson(3)   Y and Z are independent random variable

Q: If random variable X has a binomial distribution with 18 and P(success) 0.3, find the mean of X.

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Q: Let  p(y)  denote the probability function associated with a Poisson random variable with mean ?.…

A: Explanation:here given the Poisson distribution with mean 8.3   Greatest integer is 8  So the answer…

Q: The time to fly between New York City and Chicago is uniformly distributed with a minimum of 80…

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Q: From past experience, it was found out that in a certain factory, there is an average of two…

A: Let ,X=no.of accidents per monthX~poisson (λ=2)P(X=x)=e-λ λxx! ; x≥0

Q: Occasionally an airline will lose a bag. Suppose a small airline has found it can reasonably model…

A: Given that  The number of bags lost each weekday using a Poisson model with a mean of 2.2 bags  We…

Q: Ten percent of the tools produced in a certain manufacturing process turn out to be defective. Find…

A: Ten percent of the tools produced in a certain manufacturing process turn out to be defective

Q: Suppose we have a random variable X distributed as a Bernoulli distribution with p = 0.5. What is…

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Q: Explain the Covariance functions as applicable to random processes.

A: The autocovariance function CX(s,t) of a random process {X(t)} is a function of two times s and t.…

Q: Selene’s immediate superior notices that she tends to commit an average of 15 errors for every 50…

A: Givenan average of 15 error for every 50 pageserror per page = 1550=0.3per 20 pages…

Q: 2. Show how the Poisson distribution -m m e (x= 0, 1, 2,...) %3D х! can be regarded as the limiting…

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Q: If electricity power failures occur in a particular industry according to Poisson distribution with…

A: The mean is 15 so m=15 The Poisson distribution is given by: PX=r=15re-15r!

Q: Vahe, who is professor Madoyan’s favorite student, asks questions during office hours with a rate of…

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Q: Define random variables for discrete and continuous variable?

A: A random variable is a variable with an undefined value, or a function that assigns values to each…

Q: Which random variable X is a discrete variable?

A: The number of degrees of the liquid can be in decimal. It can take any real value. So it is a…

Q: A rare genetic disease is known to be carried by DD people among 10000 people in the society. a) In…

A: Given: A rare genetic disease is known to carried by DD (10) people among 10000 people.…

Q: conditions required for a random variable X to follow a Poisson process.

A: *Answer:

Q: A discrete random variable X has the mean 6 and variance 2. If it is assumed that the distribution…

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Q: Occasionally an airline will lose a baq. Suppose a small airline has found it can reasonably model…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (b) Suppose that the number of students attending certain class has Poisson distribution with mean…

A: Given,A random variable X~Poisson(λ=15)P(X=x)=e-λ λxx!   ; x≥0

Q: A  good rule of thumb for when a sample of Bernoulli trials follows a Binomial distribution is when…

A: True if statement is Correct  False if statement is Incorrect

Q: If the random variable X is distributed according to the Binomial distribution Bin(5,0.6) then…

A: Let X represent random variable   X~ Binomial(5, 0.6)

Q: Show that Poisson distribution is a limiting form of negative binomial distribution.

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Q: If a random variable X has a Poisson distribution with P(X = 1) 2P(X = 2). What is P(X = 3)? %3D 2

A: Hence,  Option (a)  e^-1/6 , is the correct✅ choice.

Q: In a binomial distribution consisting of 5 independent trials, probabilities of 1 and 2 success are…

A: Binomial Distribution :                   A discrete random variable X taking value 0,1,2,...,n is…

Q: The number of weekly breakdown of a computer is a random variable having a poisson distribution with…

A: Let us denote X=The number of weekly breakdown of a computergiven that X follows a Poisson…

Q: A grocery store normally sells 6 jars of caviar per week. Use the Poisson Distribution to find the…

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Q: If the number of minutes it takes a service stationattendant to balance a tire is a random variable…

A: Let x be the number of minutes it takes a service station time balance a tire follows exponential…

Q: If the random variable X has a Poisson distribution where the lambda equals 7, Then the probability…

A: Givenλ=7x~poisson(λ=7)P(X=x)=e-λ×λxx!   x≥0

Q: Justify and explain that if X and Y are independent random variables with respective parameters…

A: It is provided that X+Y = n and X, Y are non-negative, then X can choose 1, …, n. Therefore,

Q: Suppose that the probability of success is p in a Bernoulli trial with success x. Show that the…

A: Bernoulli Trail: In probability theory, a Bernoulli trial is a random experiment which has exactly…

Q: Assume that the number of new visitors to a website in one hour is distributed as a Poisson random…

A: Obtain the probability that in any given hour zero new visitors will arrive at the website The…

Q: If x is a random variable that has a uniform distribution in the interval [1,7].[1,7]. What is the…

A: Solution-: Let, X- be the the random variable Given: a=1, b=7 We find, P[the random variable x…

Q: The number of x people entering the intensive care unit (ICU) at a particular hospital on any given…

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Q: During a month in Adana, it rains with probability 2/3 each day, independently of every other day.…

A: Let p be the probability that it rains any day in a month. Given that p = 2/3 Let X represents the…

Q: For the probability distribution of a discrete random variables, the probabilities of any single…

A: The probability can't be exceed than 1 for any distribution.

Q: Which one of these variables is a continuous random variable?

A: Continuous variables are those variables which can take any value in an specified interval. Discrete…

Q: If the number of hurricanes that hit a certain area of the eastern United States per year is a…

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Q: The time to fly between New York City and Chicago is uniformly distributed with a minimum of 56…

A:

Q: A rare genetic disease is known to be carried by DD people among 10000 people in the society. a) In…

A: Given, DD=20 GG=2 HH=5 LL=6 p=DD/total number of people =20/10000 =0.002

Q: Obtain the maximum likelihood estimate 0 of for the probability distribution.

A: Answer: For the given data,