If `f(x)={{:(2x, 0 le x le a), (0, "otherwise"):}` is a probability density function of a random variable, then the value of a is

If f(x) = {(2x,0 lt=xlt=a),(0,"otherwise"):} is a probability density function of a random variable then the value of a is ……….. .

If f(x)= kx, 0 lt x lt 2 = 0 otherwise, is a probability density function of a random variable X , then find (i) value of k, (ii) P(1 lt x lt2).

If f(x)=1/9x^(2)0lexlta is a probability density function of random variable then the value of a is

If the probability density function of a random variable X is given as then F(0) is equal to

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)

If f(x)=ae^(-2x)0ltxltinfty is a probability density function of a random variable x then its variance is

If f(x) = (A)/(pi)(1)/(16+x^(2)),0 ltx lt oo is a probability density function of a continuous random variable X then the value of A is ……… .

The probability density function of a random variable X is f(x) = k(x-1)^2 , 1 le x le 2 . The value of the constant K is

If f(x)=k(2x-x^(2)),0lexle1 is probability density function of a continous random variable x then k is