4 96 It is known through data collection and considerable research that the amount of time in seconds that a certain employee of a company is late for work is a random variable X with density function f(x) 3 (4)(503 ) (502 x2 ), 50 x 50, 0, elsewhere In other words, he not only is slightly late at times, but also can be early to work (a) Find the expected value of the time in seconds that he is late (b) Find E(X2 ) (c) What is the standard deviation of the amount of time he is late

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Question: 4.96 It is known through data collection and considerable research that the amount of time in seconds that a certain employee of a company is

4.96 It is known through data collection and considerable research that the amount of time in seconds that a certain employee of a company is late for work is a random variable X with density function f(x) =

(4)(503 ) (502 − x2 ), −50 ≤ x ≤ 50, 0, elsewhere.

In other words, he not only is slightly late at times, but also can be early to work.

(a) Find the expected value of the time in seconds that he is late.

(b) Find E(X2 ).

(c) What is the standard deviation of the amount of time he is late?

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