Data errors can occur due to a diverse set of issues that can arise in datasets, ranging from missing data and duplicates to outliers, inconsistencies, and inaccuracies. Given the growing dependence on data$-$driven decision$-$making, rectifying data errors has emerged as a critical concern in modern data management.

A sensor records a signal every for and uses a micrcontroller to display the data. The incoming signal can be described as a function of time:

The recorded data, $,$ includes normally distibuted noise, $,$ with mean of $0$ and standard deviation of $1($you may use randn function in Matlab to create a normally distibuted noise$).$

a$.$ Calculate and plot the recorded data $($signal including noise$)$ for $.$

b$.$ Sort the data and find the minimum and maximum value of the signal with the index of time.

c$.$ Plot the time function of the sorted signal.