A1.

Please refer to the “Purchase Data” worksheet of Lab Session1 Data.xlsx. Please load the data and segregate them into 2 matrices A & C (following the nomenclature of AX = C). Do the following activities. •What is the dimensionality of the vector space for this data?

•How many vectors exist in this vector space?•What is the rank of Matrix A?

•Using Pseudo-Inverse find the cost of each product available for sale. (Suggestion: If you use Python, you can use numpy.linalg.pinv()function to get a pseudo-inverse.)

A2.

Use the Pseudo-inverse to calculate the model vector X for predicting the cost of the products available with the vendor.

A3.

Mark all customers(in “Purchase Data” table)with paymentsabove Rs. 200 as RICH and others as POOR. Develop a classifier model to categorize customers into RICH or POOR class based on purchase behavior.

A4.

Please refer to the data present in “IRCTC Stock Price” data sheet of the above excel file. Do the following after loading the data to your programming platform.

•Calculate the mean and variance of the Price data present in column D. (Suggestion: if you use Python, you may use statistics.mean()& statistics.variance()methods).

•Select the price data for all Wednesdays and calculate the sample mean. Compare the mean with the population mean and note your observations.

•Select the price data for the month of Apr and calculate the sample mean. Compare the mean with the population mean and note your observations.

•From the Chg% (available in column I) find the probability of making a loss over the stock. (Suggestion: use lambda function to find negative values)

•Calculate the probability of making a profit on Wednesday.

•Calculate the conditional probability of making profit, given that today is Wednesday.

•Make a scatter plot of Chg% data against the day of the week