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Click the link on Piazza to set up your repository for HW 5, then clone it. The repository should contain two files aside from this readme, both of which you will use in Problem 1: 1. vehicle_survey_1.txt, a text file containing the age of student vehicles on campus. 2. vehicle_survey_2.txt, a text file containing the age of student vehicles whose owners do not personally change their oil. 3. vehicle_survey_3,txt, a text file containing the age of student vehicles whose owners do personally change their oil. N Note: For both problems 1 and 2 whenever the standard error is computed we do not know the true population mean (i.e., when using np.std(data, ddof =x ), x should be set to 1) 1) Problem 1: Sampling Follow the instructions on the Writeup.pdf file, the one that you will submit to Gradescope Writeup.pdf is a .pdf with fillable fields, make sure to save the .pdf once you have entered your answers! Given the probability density function: fx(x)={23x20whenx[1,1]otherwise Use Python to plot the probability density function from 1 to 1 . When looking at the plot determine by inspection what is the mean of the distribution. Mean of the distribution: From this distribution we grab 100 i.i,d samples X1,X2,+X100 The sample mean random variable is defined as xm=n1i=1nxi We know that the variance of each xi is 53. What is the shape of the probability density function of the sample mean? What is the mean of the probability density function of the sample mean? Explain how you know the shape and mean. Part B Let X be a normally distributed random variable with mean =0 and variance =1. What is the distribution of the random variable Y=X (Give your answer with the shape, mean and variance). What is the shape of the distribution? Let X be a normally distributed random variable with mean =0 and variance =1. What is the distribution of the random variable Y=X (Give your answer with the shape, mean and variance). What is the shape of the distribution? What is the mean? What is the variance