Suppose that a pair of fair dice are rolled 120 times. Let X be the number of rolls on which the sum of the two numbers is 12. Show your working details. You may use R to verify your answer. (a) Find the probability when X = 3 approximately using Poisson approximation. (b) Compute the actual probability from binomial distribution. Comment on the accuracy of Poisson approximation.

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A: Givenμ=λ=0.3x~Poisson(λ=0.3)P(X=x)=e-λ*λxx! ; x≥0

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A: Formula : poisson distribution is given by

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A: The Binomial distribution is given by  P(x)=C(n,x) px qn-x                                    ...…

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Q: Let X be a Poisson random variable with mean 2. If P[X = 1|X <1] = 0.8, what is the value of 2?

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

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Q: Find the moment-generating function ?(?) for a Poisson distributed random variable with mean ?.

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A: Given: λ per hour = 10

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A: Poisson approximation is given by:

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

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Q: Given the binomial experiment with  n = 400  trials and probability of success on a single trial…

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Q: Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain…

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A: The above equation is in the quadratic form

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Q: Suppose that half of all students (50%) in campus dormitories are dissatisfied with the food…

A: n = 64 p = 0.5

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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.