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प्रश्न
The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for" x > 0),(0,"for" x ≤ 0):}`
Find the value of k
उत्तर
Since f is a probability density function
`int_-oo^oo f(x) "d"x` = 1
`int_oo^0 f(x) "d"x + int_0^o f(x) "d"x` = 1
`0 + int_0^oo k"e"^((- 1)/3) "d"x` = 1
`k["e"^((-1)/3)/(- 1/3)]_0^oo` = 1
`- 3"k" ("e"^-oo - "e"^0)` = 1
`- 3"k"(- 1)` =
3k = 1
k = `1/3`
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