Suppose that X is a Poisson random variable with i = 12.Round your answers to 3 decimal places (e.g. 98.765).(a) Compute the exact probability that X is less than 8.(b) Use normal approximation to approximate the probability that X is less than 8.Without continuity correction: iWith continuity correction:i(c) Use normal approximation to approximate the probability that 16 < X < 24.Without continuity correction:With continuity correction: i

We have given that X~Pois(λ=12) The pmf of Poisson distribution is (a)P(X=x) = e-λλx/x! ;…

Answered: Suppose that X is a Poisson random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The pdf of the time to failure of an electronic component in a copier (in hours) is f (x) = [exp (-x/3100)]/3100 for x > 0 and f (x) = 0 for x ≤ 0. Determine the probability that:(a) A component lasts more than 1180 hours before failure.(b) A component fails in the interval from 1180 to 2010 hours.(c) A component fails before 3010 hours.(d) Determine the number of hours at which 11% of all components have failed.(e) Determine the mean.Round your answers to three decimal places (e.g. 98.765).
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Exercise 10. For an exponential random variable X (Definition 10), show that E[X] = }. More generally, for a function o : R R, E(¢(X)] = | (u) dF(u) (5.4)
The random variable X has expected value E(X)=4 and Var(X)=4. Here, we want to approximate the probability that X lies in the interval [3.4,5.4] using a transformation to a standard normal distribution Z. Then we will need to calculate the probability that Z lies in the interval [z1,z2] where z1= z2= Suggest z1 and z2 Do NOT attempt to make any sort of continuity correction.

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