Find k if the function f(x) is defined by : f(x)=k x(1-x), for 0<… - Vidyadip

Question

Find $k$ if the function $f(x)$ is defined by :
$f(x)=k x(1-x), \quad$ for $0<x<1$
$=0$, otherwise.
is the probability density function (p.d.f.) of a random variable (r.v.) X. Also find $P\left(X<\frac{1}{2}\right)$

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