The c. d. f. $F(x)$ associated with p. d. f. $f(x)=3\left(1-2 x^{2}\right)$ if $0 < x < 1$ $=0$ otherwise is…
The c. d. f. $F(x)$ associated with p. d. f. $f(x)=3\left(1-2 x^{2}\right)$ if $0 < x < 1$
$=0$
otherwise
is $k\left(x-\frac{2 x^{3}}{k}\right)$, then value of $k$ is
3
1
$\frac{1}{3}$
$\frac{1}{6}$
Solution
Since $f(x)$ is p.d.f. of r.v. therefore c.d.f. is
$F(x)=\int_{0}^{1} 3\left(1-2 x^{2}\right) d x=\left[3\left(x-\frac{2 x^{3}}{3}\right)\right]_{0}^{1}$
From given data, we get $k=3$