Question 2(a)The probability density function (PDF)of a continuous random variable X isgiven by f(x)=2e for x>0.Analyze and determine the value of the 0.1-Table Q2(e)presents the survey results of a sample of 1000 households in termsquantile.of purchase behaviour for cordless vacuum cleaners.(3 marks)Actually purchasedPlanned to purchase(C)In a particular factory,a day's production of 850 manufactured parts contains 50YesNoparts that do not meet customer requirements.Two parts are selected at random.Yes20050without replacement.from the batch.Let X denotes the event that the first part isNo100650defective.Let Y denotes the event that the second part is defective.Analyze anddetermine P(Y X).Table Q2(e)(2 marks)()Analyze and compute the probability that a household planned to purchaseor actually purchased a cordless vacuum cleaner.(d)Eight cavities in an injection-molding tool produce plastic connectors that fall(2 marks)into a common stream.A sample is randomly chosen each time.Assume that thesamples are independent.Solve and compute the probability that five successive(Analyze and compute the probability that a household actually purchasedsamples were all produced in the same cavity of the mold.the cordless vacuum cleaner,given that he or she planned to purchase.(5 marks)(2 marks)