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Question
State whether the following is True or False :
If f(x) = k x (1 – x) for 0 < x < 1 = 0 otherwise k = 12
Options
True
False
Solution
False
Since the function represents a p.d.f. 1
∴ `int_0^1 f(x)*dx` = 1
∴ `int_0^1 "k"x (1 - x)*dx` = 1
∴ `"k" int_0^1 (x - x^2)*dx` = 1
∴ `[x^2/2 - x^3/3]_0^1 = (1)/"k"`
∴ `(1)/(2) - (1)/(3) = (1)/"k"`
∴ `(1)/(6) = (1)/"k"`
∴ k = 6.
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