For p.d.f. $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ (and 0 elsewhere…

Question

For p.d.f. $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ (and 0 elsewhere), the value of $k$ is:

Accepted Answer

D. $3/32$

$\int_{-2}^2 k(4 - x^2)\,dx = k[4x - x^3/3]_{-2}^2 = k\{(8 - 8/3) - (-8 + 8/3)\} = k \cdot 32/3 = 1$ ⇒ $k = 3/32$.

Answer

$3/16$

Answer

$1/8$

Answer

$1/16$

For p.d.f. $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ (and 0 elsewhere), the value of $k$ is: