Find k, if the function f defined by `f(x) = kx, 0 lt x lt 2` =0 , otherwise is the p.d.f of a random variable X.

Find k if the function f(x) is defined by f(x)=kx(1-x),"for "0ltxlt1 =0 , otherwise, is the probability density function (p.d.f.) of a random varible (r.v) X. Also find P (Xlt(1)/(2))

If the function f(x) =(x^(2))/(3), - 1lt x lt 2 = 0 , otherwise is a p.d.f of X, then P(X lt 0) is

If f(x) = k x (1 -x) , for 0 lt x lt 1 = 0 , otherwise , is the p.d.f. of a r. v. X then k = 12 . True or False.

Show that the function f(x) defined by . f(x) = (1)/(7) , for 1 le x le 8 =0, otherwise, is a probability density function for a random variable. Hence find P(3 lt Xlt 10)

Find k, if the following is p.d.f or r.v.f X. f(x) = {{:(kx^(2)(1-x), 0 lt x lt 1),(0, "otherwise"):}

The following is the p.d.f of continuous random variable X. f(x) = (x)/(8), 0 lt x lt 4 =0 , otherwise. Find the expression for c.d.f of X

The following is the p.d.f (Probability Density Function ) of a continous random variable X : f(x) = (x)/(32), 0 lt x lt 8 = 0 , otherwise Find the expression for c.d.f (Cumulative Distribution Function ) of X

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 following is the p.d.f (Probability Density Function ) of a continous random variable X : f(x) = (x)/(32), 0 lt x lt 8 = 0 , otherwise Also, find its value at x = 0.5 and 9.