Find `k, P (X lt 1), P (0 lt x lt 3).`

The p. d. f. of a continuous r. v. Xis f(x) = {:((3x^2)/8 , 0 lt x lt 2),(0, "otherwise"):} Determine the c.d.f of X and hence find (i) P(X lt 1), (ii) P(1 lt X lt 2) .

A random variable X has the following probability distribution: Determine (i) k (ii) P (X lt 3) (iii) P (X gt 6) (iv) P (0 lt X lt 3)

If p.d.f, of continuous random variable X is f(x) = {(2x^3,;0 lt= x lt=1), (0,;" otherwise"):}. Find P (X lt= 0.5) and P (0.5 lt= X lt= 1)

A random variable X has the following probability distribution: Determine (i) k, (ii) P(X lt 3) ,(iii) P(0 lt X lt 3), (iv) P (X gt 4) .

The p.d.f of continuous random variable X is given by f(x)=x/8,0 lt x lt 4 =0 otherwise. Find (i) P(X lt 2) (ii) P(2 lt X le 3) ( iii) P( X gt 3.)

A random variable X has the following probability distribution. i. k ii. P(X lt 3) iii. P (0 lt X lt 5)