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Question
A commuter train arrives punctually at a station every half hour. Each morning, a student leaves his house to the train station. Let X denote the amount of time, in minutes, that the student waits for the train from the time he reaches the train station. It is known that the pdf of X is
`f(x) = {{:(1/30, 0 < x < 30),(0, "elsewhere"):}`
Obtain and interpret the expected value of the random variable X
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Solution
Given, p.d.f. is `f(x) = {{:(1/30, 0 < x < 30),(0, "elsewhere"):}`
‘X’ is a continuous random variable.
∴ Expected value of X = E(X) = `int_0^30 x f(x) "d"x`
= `int_0^30 x 1/30 "d"x`
= `1/30 [x^2/2]_0^30`
= `1/30[(30 xx 30)/2 - 0]`
= 15 minutes
The average waiting time for the student is 15 minutes.
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