Task 1: (50 marks)The time between hits to a particular website (BetweenHitTimes) is thought to follow anExponential distribution. The times between hits, measured in minutes, are in the fileSiteHitTimes_n70.sav.(a) For the data file of site hit times in minutes produce a stem-and-leaf plot, histogram andboxplot. Comment on the shape of the distribution and identify any outliers.(b) Determine the basic summary statistics: minimum, maximum, mean, median, standarddeviation and variance. Compare the value of the mean and the median. Compare thevalue of the mean and standard deviation.(c) The time between hits to a particular website (BetweenHitTimes) is thought to follow anExponential distribution. What two features identifiable in the plots and summary statisticsoutput suggest that the time between time between hits is exponentially distributed?(d) Show how the exponential model is calibrated confirming that the estimate for λ (lambda) is0.38 correct to two decimal places. Use this λ in later calculations.(e) Using your estimate of lambda (0.38), calculate the expected value of the time between hits,that is find E(Y) where Y ~ Exp(0.38).(f) Determine the (theoretical) variance and standard deviation of Y, the time between hits,correct to two decimal places.(g) Calculate the probability that the time to the next hit is between 0 and 1 minute (correct tofour decimal places).(h) Calculate the probability that the time to the next hit is between 1 and 2 minutes (correct tofour decimal places).