Once again you have forgotten the password to your email account. Upon clicking the forgot password linlt you are instructed to wait for a text...

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Once again you have forgotten the password to your email account. Upon clicking the forgot password linltyou are instructed to wait for a text message with the information to reset your password. Suppose youremail provided claims this will take approximately between 1 and ill minutes. More specifically let’s assume the random variable X is the time this message takes to reach your phone, where X has the following probability,r density function:III): flay-3 14114.1“99“ ’ otherwisea. {Optional Not Graded) 1iWet-if); that fix) is a valid probabflity dusity function.b- {1 point) 1‘1 331131311 according 1“ the graph ““113 'I'lme tor password reset message probabifity density fimction is it more likely the textmessage will arrive at the beginning of the time interval orat the end? (Want to brow how to make this graph? Seecarafe in Data Analysis I) {3 points] What is the average time it will take to receivethe message? Calculate E{X}. Must show all 1.5 2.0 Hi {3 points] How much does the time to receive the message 3 deviate from the average? Calculate SDtX]. Must show all g work. ‘5 {3 points] What is PIX}, the cumulative density fimction of 3 4 5 3 “IX? Must show all work. “m {3 points] You’re impatient, what is the chance this textmessage will take longer than 2 minutes to arrive? Use either F{X] or fix) and show work.{Optional Not Graded) What is the median time it takes to receive the message? Does this value make sense in relation to the average?