Question

A continuous random variable x follows the probability law. f (x) = Ax³, 0 < x < 1 determine A.

Answer 1

A continuous random variable x follow the probability law,
when $\int\limits^{\infty}_{-\infty}{f(t)}\,dt$ = 1

Here , f(x) = Ax³ , 0 < x < 1
so, $\int\limits^{\infty}_{-\infty}{f(x)}\,dx = \int\limits^{1}_0{Ax^3}\,dx$ = 1
⇒A[ x⁴/4]¹₀ = 1
⇒ A[ 1/4 - 0] = 1
⇒ A/4 = 1
⇒A = 4

Hence, value of A = 4