Let X, the number of flaws on the surface of a randomly selected boiler of a certain type, have a Poisson distribution withparameter u = 5. Use the cumulative Poisson probabilities from the Appendix Tables to compute the following probabilities.(Round your answers to three decimal places.)(a) P(X S 8)(b) P(X = 8)(c) P(9 < X)(d) P(5 S X S 8)(e) P(5 < X < 8)

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Answered: Let X, the number of flaws on the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Q 4.4. An individual picked at random from a population has a propensity to have accidents that is modelled by a random variable Y having the gamma distribution with shape parameter a and rate parameter 3. Given Y = y, the number of accidents that the individual suffers in years 1, 2, ..., n are independent random variables X₁, X2,... Xn each having the Poisson distribution with parameter y. (a) Write down a function f so that the joint distribution of Y, X₁,..., Xn can be described via =ff(y, k₁, k₂.. f(y, k₁, k2, ... kn)dy P(a ≤ Y ≤ b, X₁ = k₁, X2 = k2 … . . Xn = kn) = [. .. and derive from this expression that, for your choice of f, Y has the Gamma distribution, and that conditionally on Y = y, X₁, X2,... Xn are independent, each having the Poisson distribution with parameter y. (b) Find the conditional distribution of Y given that X₁ = k₁, X2 = k2, . . . , kn.
Previous records have indicated that the number of rejected eggs per crate follows the Poisson distribution with mean 1.5. For the data 4, 0, 2, 0, 2, 0, 2, 0, test the hypothesis that these eight crates came from the same distribution function. Note that the Poisson distribution with mean 1.5 has the following probabilities: P(0) = 0.223, P(1) = 0.335, P(2) = 0.251, P(3) = 0.126, P(4) = 0.047, P(5) = 0.014, and P(6) = 0.004.
Suppose that arrival times at a certain emergency care center are following a Poisson process with a mean rate of λ = 0.2 arrivals per minute. Let T be the time until the third arrival. Find the mean and the variance of T, and find P(T ≤ 10) to four decimal places. Part 1 out of 3The mean of T is _______minutes.
A Poisson distribution with λ =7.4 λ =7.4 and x=5Use the probability distribution identified above to calculate the following:
Q3. A random variable X is normally distributed with µ= 50 and o² = 25 . Find the %3D Probability (a) that it will fall between (i) 0 and 40 (ii) 55 and 100 (b) that it will be (i) large than 54 (ii) smaller than 57
55. Given this joint pmf, (a) Find the conditional distribution of X given Y = 0, fxY=0(x) = P(X=x|Y = 0). (b) Are X and Y independent? Justify your answer.
2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1
Q 4.4. An individual picked at random from a population has a propensity to have accidents that is modelled by a random variable Y having the gamma distribution with shape parameter a and rate parameter ß. Given Y = y, the number of accidents that the individual suffers in years 1, 2, ..., n are independent random variables X₁, X2,... Xn each having the Poisson distribution with parameter y. (a) Write down a function f so that the joint distribution of Y, X₁, Xn can be described via P(a ≤ Y ≤ b, X₁ = k1, X₂ = k2 … . . Xn = kn) = [° ƒ (y, k1, k2, ... kn)dy and derive from this expression that, for your choice of f, Y has the Gamma distribution, and that conditionally on Y = y, X₁, X2,... Xn are independent, each having the Poisson distribution with parameter y.
6. Consider an Exponential Distribution with parameter m = 0.2 D. Compute the following Probabilities IV. P(X 15 | X > 10)
Q.6. Use the binomial distribution in which n 6 and p = 0.3 to %3D calculate the following probabilities: (a). X is at most 1. (b). X is at least 2. (c). X is more than 5. (d). X is less than 6.
Let X1, X2......,X100 be independent binomial random variables with parameter p=0.25. The sample mean is : (First image) a. Find the value of E(X) and Var(X). b. State the sampling distribution of X and explain why has the sampling distribution stated. c. Find P(X<25.5). d. Find (second image)
Let X₁,... Xn be sampled from a uniform distribution with support 0≤x≤0. a. Find the PDF of the second ordered statistic X(2) b. Find the expected value of X(2). You may use wolfram, but you must correctly write down what you are asking Wolfram to calculate for you. c. Find an unbiased estimator of 0, that is a function of X(2).

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