Use the data set assigned to your student ID and design a MATLAB script file to do the following (Hint: save the text file in your main folder and use the command "importdata" in your script file to load the data file: X = importdata('xxxxx.txt'). The vector X will contain the data saved in the text file). 1. Compute and display the mean , variance, and the standard deviation of the data. (8 marks) 2. Generate (but do not display) the probability density function (PDF) and the cumulative distribution function (CDF) that represents the data. (8 marks) (8 marks) 3. Plot both PDF and CDF functions. 4. Compute the following probabilities: a. P(X> +20) (5 marks) b. Pu-ox+20) (5 marks) s. If the random variable X is transformed according to the linear transformation Y= a X+b where a and b are constants: a. For a=2 and b=3, find the mean and the variance of the random variable Y and display them. (4 marks) b. Generate and plot the probability density function (PDF) for Y. (3 marks) c. Design a for loop to plot the probability density of the random variable Y for the range of a and b as follows: a = 1:2:10 and b = 0:2:10. (5 marks) 11.23470946 23.46151668 -0.403588512 5.756052378 21.50532472 24.52642002 24.95547574 17.9893142 18.86940454 3.727375851 16.83716932 16.90711841 11.07443688 34.64076071 28.31971556 14.6570928 3.010319261 12.02370752 19.63201297 32.29156739 23.40156281 8.027527627 8.44546806 19.21139352 5.352365552 18.88768463 30.04838955 13.06659393 17.78238599 9.914190238 23.11742165 19.16762279 50.62287481 26.65103391 19.13660718 45.02611492 40.81907098 14.66840003 21.89934645 0.216496183 17.39160691 16.59876377 -15.97347607 14.60033387 38.53916276 26.87044508 12.31891487 11.07041775 4.745791003 1.047149647 35.10492789 51.50634374 4.269365075 16.65591343 27.40431385 31.76091094 22.15811858 11.0968454 15.29209873 28.92701741 34.02595923 7.371927845 12.01572796 5.367976216 13.22323134 11.52957434 30.69333394 26.97126199 49.22101725 13.53826301 18.01624751 6.794056085 5.605428871 22.90046377 9.463333462 23.8416922 20.39955003 19.16777546 14.9546053 21.12387497 4.555604519 36.83691296 15.23016253 3.936893159 17.74961607 43.91836523 27.09297039 34.2235511 20.56525422 6.175328743 0.261508644 22.70499427 7.53066545 31.7656561 11.99032815 26.88877859 22.25712821 0.771069331 15.22335797 24.25900378 5.845089283 52.7796059 12.49517315 49.56439494 0.1847136 17.1159322 33.14019132 17.70727556 20.76484735 -12.42269396 8.691557274 26.4927226 39.61065004 36.27749735 29.59450212 52.1185374 23.08456626 19.42871431 24.05531761 21.96222019 52.40551449 19.86222145 19.72974894 31.79201532 31.20410713 16.1150136 3.79058231 17.55668217 15.73382711 12.42405582 6.671711299 36.75242447 9.837310092 19.39319186 15.44379132 13.76369739 8.469868526 23.83347946 32.29772639 21.87309966 17.39712679 23.84125702 5.256859142 6.011839154 5.034788222 21.63300833 8.444680777 32.9025026 40.20237728 35.57458636 27.63508872 11.83698668