STAT273: Memoryless Property - Normal Approximation to Poisson Distribution - R Programming Assessment Answer

R Programming Assessment Task

STAT273

Question1 (Memoryless Property) STAT273
We know that the memoryless property holds for the geometric and the exponential distributions (see Q3, SGTA Week 8). Assume that the time T between job submissions to a busy computer centre is uniformly distributed in the range [0, 0.5] min. Using R, show that in this case the memoryless property does not hold.
Question 2 (Normal Approximation to Poisson Distribution) STAT273
Use R to illustrate the normal approximation to Poisson distribution, Poisson(?). Choose how to measure a distance between two distributions (the smaller the distance is, the better approximation will be). For example, you may use the ?2 goodness-of-fit test statistic; see Q1 (SGTA Week 11). Carry out a thorough simulation study and decide on how big ? should be for this approximation to work (your “rule of thumb” might give a minimum value of ?). Show your reasoning.

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