If F `(x)=1/pi(pi/2+tan^(-1)x)-ooltxltoo` is a a distribution function of a continuous variable X find P `(0 le x le 1)`

F(X)=(pi)/(2+tan^(-1))(x)/(pi)-inftyltxltinfty is a distribution of a continous random variable X then P(X le 1) 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 cumculative distribution function of a discrete random variable is given by F(x)={{:(0, "for "-infty lt x lt 0), ( 1/2, "for " 0 le x lt 1), (3/5, "for " 1 le x lt 2), (4/5, "for " 2 le x lt 3), (9/10, "for " 3 le x lt 4), (1, "for " 4 le x lt infty):} Find (i) the probability mass function (ii) P(X lt 3) and (iii) P(X ge 2) .

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 X is the random variable with distribution function F(x) given by, F(x)={{:(0, x lt 0), (1/2(x^(2)+x), 0 le x lt 1), (1, x le 1):} then find (i) the probability density function f(x) (ii) P(0.3 le X le 0.6)

If X is the random variable with probability density function f(x) is given by f(x)={{:(x+1, -1 le x lt 0), (-x+1, 0 le x lt 1), (0,"otherwise"):} then find (i) the distribution function F(x) (ii) P(-0.5 le X le 0.5)

The value of sin^(-1) (cos x ) , 0 le x le pi is :

Find the range of the function f(x) = [ 2 x ] , 1/3 le x le (8)/(3)