Let x be a Poisson random variables. Find the probabilities for x using the Poisson Form

Q: Let X be a binomial random variable with probability distribution 3-a SOOʻO**, x = 0,1, 2, 3, f(x) =…

A: Solution-: Given: n=3,p=2/5 ∴X→B(n=3,p=2/5) The p.m.f. of X is given by,  P(X=x)=3x*(25)x*(35)3-x…

Q: In 1985, neither Florida nor Georgia had laws banning open alcohol containers in vehicle passenger…

A: (i) Consider FL be a dummy or binary variable which is equal to one if a person lives in Florida,…

Q: Find the expectation of a discrete Random variable whose probability function is fx (x) = for x = 1,…

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Q: The number of telephone calls that arrive at a phone exchange is often modeled as a Poisson random…

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Q: Let X be a Poisson random variable with parameter λ. Prove that the probability that X is even is…

A: Given that, X be a Poisson random variable with parameter λ. We need to show that the probability…

Q: When packaging a product, a manufacturer finds that one packet in 20 is underweight. Using Poisson’s…

A: Probability of one packet is underweight i.e 120. Also n=71. As the number of packet is underweight…

Q: Decide whether the random variable x is discrete or continuous. x represents the length of time it…

A: We know that discrete variables take a finite number of countable points whereas a continuous random…

Q: . Let a random variable X - U(5,5+0). Based on a single observation X1, find the unbiased estimator…

A: # random variable x follow uniform (5,5+theta) then to find unbiased estimator of theta^2

Q: 2. Define the characteristic function of a random variable and state its properties.

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Q: Assume that 12 jurors are randomly selected from a population in which 86% of the people are…

A: The probability of exactly 7 Mexican Americans among 12 jurors is obtained below: P(x=7)=0.0148.

Q: Assume a random variable X follows a Poisson distribution with a mean μ=2.6 P(X≤3)=  Round each…

A: Given : a random variable X follows a Poisson distribution with a mean μ = 2.6 The formula for…

Q: A corporation has 250 personal computers. The probability that any 1 of them will require repair in…

A: Given,n=250p=0.01mean=λ=npλ=250×0.01=2.5A random variable X~Poisson(λ=2.5)P(X=x)=e-2.5 2.5xx!  ; x≥0

Q: Prove that f_x is a true probability function, find its expected value and its variance

A: HERE FOR VALID PROBABILITY DISTRIBUTION FUNCTION TOTAL PROBABILITY IS ALWAYS EQUAL TO 1

Q: According to a survey, 31% of employees working at a very large company are happy with their jobs.…

A: 31% working employees of a large company are happy with their jobs. So, probability that an employee…

Q: d) Use Poisson approximation to find the probability that the sample contains at most 1defective…

A: Binomial Distribution: If we have n trials each having two outcomes, say Success and Failure, trials…

Q: < 400ml 2 400ml total Low sugar available No low sugar 45 35 80 15 105 120 Total 60 140 200

A: We use the given contingency table to find the required probability.

Q: According to an Allstate Survey, 56% of baby boomers have car loans and are making payments on these…

A: Let X denote the number in a random sample of three baby boomers who are making payments on their…

Q: Let the random variable X represent the number of cars that are used for official business purposes…

A: Consider, μA=∑xPA(x)     =(1*0.3)+(2*0.4)+(3*0.3)     =2 σA=∑x2PA(x)-∑xPA(x)2…

Q: Let X, Poisson(A,), for i = 1, 2. (a) Show that X1+ X2 ~ Poisson(A1+ A2). (b) Show that X1 | X1 + X2…

A: Introduction: If X ~ Poisson (λ), where λ is the rate of occurrence of the event of interest in a…

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: Suppose the probability of a major earthquake on a given day is 1 out of 20,000. Complete parts a…

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Q: A vending machine in a supermarket breaks down an average of four times per month. Using the Poisson…

A: Given,The average breaks down per month(λ)=4A random variable X~Poisson(λ=4)P(X=x)=e-44xx!  ;  x≥0

Q: )A random variable is defined as 1/70 (2x − 1); X = - 1,2,3,4,5,6. Construct the probability…

A: Total no of observations (n) = 6 X = 1, 2, 3, 4, 5, 6 P(X=x) = (2x-1)/70

Q: Let X be a discrete random variable with probability function P[X = x] = 3 ,x = 1, 2, 3, .. ... What…

A: Since , the probability function is given by ,  Our aim is to find the probability that X is odd.

Q: Suppose that X is a Poisson random variable with A = 6. (a) Compute the exact probability that X is…

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Q: Suppose that a random system of police patrol is devised so that a patrol officer may visit a given…

A: Let us define the random variable Y as the of number of times petrol officer may visit the beat…

Q: Assume that 12 jurors are randomly selected from a population in which 74% of the people are…

A: To find the required probability from the given probability distribution table.

Q: For any continuous random variable, the probability that the random variable takes on exactly a…

A: The probability distribution of a continuous random variable X is an assignment of probabilities to…

Q: Exercise: Xì,.,Xn are independent Poisson random variables with mean >, Find UMVUE for A

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Q: A machine manufactures 300 micro-chips per hour. The probability an individual chip is faulty is…

A: Given, A machine manufacturer 300 micro-chips per hour. The probability an individual chip is faulty…

Q: The number of accidents at a certain intersection is a Poisson random variable. The probability that…

A: we have given that  The probability that there are 2 accidents in any given week is 3 times as much…

Q: A laundry shop averages 5 customers per hour. Assume that the number of customers is a Poisson…

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Q: The probability distribution of a discrete random variable X is given: -2 -1 2/8 | 2/8 | 1/8 2/8…

A: We first calculate Var(X)

Q: If a Poisson random variable has a μ = 0.9. Use the Poisson table (Table 2) to find the following…

A: From the provided information, µ = 0.9 The probability distribution function of Poisson distribution…

Q: a) A player will win if he rolls two dies and gets a sum equal to 6. If he plays 12 times, what is…

A: Solution: a) A Player wins if he rolls two dice and gets a sum 6. The total number of outcomes when…

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: Let X be a Poisson random variable with parameter 2. (i) What is the probability P(X > 1)? (ii) What…

A: Solution: From the given information, X follows Poisson distribution with parameter 2. That is, λ=2.…

Q: Assume that 12 jurors are randomly selected from a population in which 80% of the people are…

A: From the hypotheses can be constructed as: The required probability of exactly 7 Mexican-American…

Q: If 5% of the electric bulbs manufactured by a company are defective, use Poisson distribution to…

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Q: The number of telephone calls that arrive at a phone exchange is often modeled as a Poisson random…

A:

Q: A mail-order company receives an average of five orders per 500 solicitations. If it sends out 100…

A: A mail order company receives an average of five orders per 500 solicitations.

Q: At a pre-school 54% of children prefer the colour red over the colour green. From a sample of 20…

A: Let x denotes the percentage preference of the color red against the color green. Then, the random…

Q: Assume that 12 jurors are randomly selected from a population in which 86% of the people are…

A: x P(x) 0 0+ 1 0+ 2 0+ 3 0+ 4 0+ 5 0.0004 6 0.0028 7 0.0148 8 0.0569 9 0.1553…

Q: For the probability distribution of a discrete random variables, the sum of the probabilities of all…

A: For the probability distribution (discrete) to be valid, the following conditions must follow- Each…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.