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)`

If the p.d.f of a continuous random variable X is f(x)=kx^(2)(1-x), 0 lt x lt 1 = 0 otherwise Then the value of k is

If the p.d.f of a continuous random variable X is f(x)=kx^(2)(1-x), 0 lt x lt 1 = 0 otherwise Then the value of k is

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.)

The p.d.f. of a continuous random variable X is f(x) = K/(sqrt(x)), 0 lt x lt 4 = 0 , otherwise Then P(X ge1) is equal to

The p.d.f. of a continuous random variable X is f(x) = K/(sqrt(x)), 0 lt x lt 4 = 0 , otherwise Then P(X ge1) is equal to

The p.d.f of a continuous random variable X is f(x) = (x^(2))/(3), - 1 lt x lt 2 0 = otherwise Then the c.d.f of X is

The p.d.f of a continous random variable X is f(x)=x/8, 0 lt x lt 4 =0 , otherwise Then the value of P(X gt 3) is

The p.d.f of a continous random variable X is f(x)=x/8, 0 lt x lt 4 =0 , otherwise Then the value of P(X gt 3) is

Thep.d.f of a continous random variable X is f(x) = (x^(2))/(3), - 1 lt x lt 2 0 = otherwise Then the c.d.f of X is

The p.d.f. of a continuous r.v. X is f(x)={{:((x^(2))/(3)","-1lt x lt 2),(0", otherwise"):} , then P(1 lt X lt2) =