If the c.d.f (cumulative distribution function) is given by `F(x)=(x-25)/(10)`, then `P(27 le x le 33)=` . . .

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)

Following is the distribution function F(x) of a X. Find P (X le 3),P(2 le Xle 5)

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 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)

For the following distribution function F(x) of a r.v. X P(3 lt X le 5)=

For the following distribution function F (X) of a r.v. X P(3 lt X le 5)=

Let f(x) and g(x) be two functions given by f(x)=-1|x-1|,-1 le x le 3 and g(x)=2-|x+1|,-2 le x le 2 Then,

Let f(x) and g(x) be two functions given by f(x)=-1|x-1|,-1 le x le 3 and g(x)=2-|x+1|,-2 le x le 2 Then,

Find the intervals in which the function f given by f(x)=sin x + cos x(0 le x le 2 pi) is decreasing

Find the intervals in which the function f given by f(x)=sin x + cos x(0 le x le 2 pi) is increasing