Answer to Question #171283 in Statistics and Probability for Ernest

Question

F(x,y)={k(1-x^2) find the value of k

Answer 1

Since f(x) is a p.d.f. $\int_{\infty}^{\infty} f(x)dx=1$

$\implies \int_0^1 k(1-x^2)dx=1$

$\implies k(x-\dfrac{x^3}{3})_0^1=1$

$\implies k(1-\dfrac{1}{3})=1$

$\implies k=\dfrac{3}{2}$