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Question
The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for" x > 0),(0,"for" x ≤ 0):}`
Find P(5 ≤ X)
Solution
P(5 ≤ X) = `int_5^oo f(x) "d"x`
= `k int_5^oo "e"^((-x)/3) "d"x`
= `1/3["e"^((-x)/3)/((-1)/3)]_5^oo`
= `- ("e"^-oo - "e"^((-5)/3))`
= `"e"^((-5)/3)`
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