ABSTRACT
Statistics, Signal Processing, Data Analysis 1. (a) Assume normal distribution in the following form f x ae x( ) ( )= - -ms 222 where m is average or mean and s is standard deviation. Calculate the parameter a such that normal distribution is normalized to 1. Hint: Integrate above function from –• to +•. The obtained
result should be equal 1. You will find that this parameter is independent of m but it depends on s. (b) How would you calculate probability that single measurement will give number that is within m ± ks where
k is positive integer number? Hint: Integrate above function from m – ks to m + ks to obtain desired probability. (c) Imagine that data are collected during Day 1 and Day 2 of an experiment. Assume that data for each day can be reliably described with normal distribution. If you know number of measurements N, means and standard deviations for both Day 1 and Day 2 how would you estimate the normal distribution that most reliably describes joint result?
