Let X be the continuous random variable of the time students have to wait for Pr
ID: 3366837 • Letter: L
Question
Let X be the continuous random variable of the time students have to wait for Prof. Nvarez to arrive to dass. The t wait time, X, is unilformly distributed. Suppose X ranges between negative means Prof. lvarez arrived early to class and a pesitive means Prof. lvarez arrived late to class What is the Probability that Prof. Alvarez arrives exactly on tine, PX-o? What is the Probability that Prof. Alvarez arrives between -5 to 0 minutes early? What is the Probability that Prof. Alvarez arrives between-4.1 to 4.9 minutes early? Find the mean wait time for students. CRound to four dedimal places) (Round to four decimal places.) Round to four decimal places (Round to four decimal places.) Find the standard deviation wait time for students. a- (Round to four decimal places) Sumit Answer Save Progress Pradice Another VersionExplanation / Answer
Cumulative distribution function, F(x) = { x - (-5)}/{5 - (-5)}
=(x + 5)/10 for x = [-5,5]
(a) P(X = 0) = 0 [Since, for any continuous random variable, the probability to take a particular value is 0)
(b) P( -5 < X < 0) = F(0) - F(-5) = 5/10 + 0 = 0.5
(c) P(-4.9 < X < -4.1) = F(-4.1) - F(-4.9) = 0.9/10 - 0.1/10 = 0.08
(d) Students need to wait only when the Prof. arrives late in the class i.e. when x = [0,5]
Thus, mean wait time for students = (5 + 0)/2 = 2.5 minutes
(e) Variance wait time for students = {(5 - 0)^2}/12 = 25/12
Thus, standard deviation wait time for students =?(25/12) = 1.4434 minutes
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