3- For this section, we will study the probability distribution for Italy. It is assumed that...

3- For this section, we will study the probability distribution for Italy. It is assumed that the confirmed cases show a normal distribution behavior. Find the mean and the standard deviation.

Consider the period between Feb, 22 and June, 22. This period is considered as the lock down period in Italy. The mean and the standard deviation gives an idea about the period to spread the virus and time required to diminish the strength of the COVID-19
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Expert Solution

As we see, the variable of our interest is the number of confirmed cases of the covid 19. So if X is a random variable representing number of confirmed cases in Italy then X is following Normal distribution with mean m and variance sigma square (s2). Now if population parameter are unknown, then thesecan be estimated from sample of suitable size so as it can best estimate the population parameter. Mean m can be estimated by its unbiased estimator sample mean xm and population standard deviation is estimated by its unbiased estimator S square i.e. sample variance. Xm=Xi /n ,

S2 =(Xi-Xm)^2/n-1

Suppose we divide the data into 2 parts :group contains data on number of confirmed cases before lockdown and another group consists of number of cases post lockdown. Now, say m1 is mean value for group 1 and m2 is mean value for group 2. We can apply testing procedures like z test ir t test to check if there is any significant difference between the 2 means or if there is any effect of lockdown or not. Then, in order to predict when the number of cases wil diminish , we can fit a regression model where dependent variable can be taken as number of confirmed cases and independent variables can be taken as various factors affecting it like immunity of person, healthcare facility ,time etc. The study of standard deviation will give the spread in data, where the cases got peak and how deviated the values are from mean value.

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orchestra answered 2 years ago

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