2. Whether you have had a course on statistics or not, you are likely to have heard of the normal (or bell) curve. Thisis what is referred to in statistics as a probability distribution which are used to calculate probabilities. In particularthe normal distribution is defined by the probability density function, with mean = 0 and standard deviation = 1.(Take a moment and graph this function to see why it's referred to as a 'bell curve'.)Using functions such as these, we may calculate probabilities by simply calculating the area under the graph of thisfunction. For example, it can be shown thatFLOwhich can be interpretted as the probability of a value falling between -∞ and ∞o, in a normally distributed set ofdata, is 1 (or 100% probability). We'll now calculate the probability that a student's exam score falls within onestandard deviation from the overall average. (In other words, with some scaling, the probability of scoring ±10 from75 if the exam scores fit a standard bell curve)(a)Using a known Maclaurin series, find a series representation centered at c = 0 for f(x) = e-7²².(b)1f(x) =√2π(c)Integrate the series you found to computePut your answer in sigma notation.dx = 1Let de-1Find an approximation to this sum with accuracy < 0.00005.

Given the normal distribution defined by the probability function fx=12πe-12x2

2. Whether you have had a course on statistics or not, you are likely to have heard of the normal (or bell) curve. This is what is referred to in statistics as a probability distribution which are used to calculate probabilities. In particular the normal distribution is defined by the probability density function, with mean = 0 and standard deviation = 1. f(x) = -√² (Take a moment and graph this function to see why it's referred to as a 'bell curve'.) Using functions such as these, we may calculate probabilities by simply calculating the area under the graph of this function. For example, it can be shown that AL e-²²dr = 1 which can be interpretted as the probability of a value falling between -∞o and ∞o, in a normally distributed set of data, is 1 (or 100% probability). We'll now calculate the probability that a student's exam score falls within one standard deviation from the overall average. (In other words, with some scaling, the probability of scoring ±10 from 75 if the exam scores fit a standard bell curve) (a) Using a known Maclaurin series, find a series representation centered at c = 0 for f(x) = -¹² (b) (c) Integrate the series you found to compute Put your answer in sigma notation. Lete de Find an approximation to this sum with accuracy < 0.00005.

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...