The probability density function of X is f(x) = `{(x,0 ltxlt1),(2-x, 1lt=xlt2),(0,"otherwise"):}`
Find (i) `P(0.2 lt=X lt0.6) (ii) P(1.2lt= X lt 1.8) (iii) `P(0.5 lt=X lt 1.5)`

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(0.2 le X lt 0.6)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(0.5 le X lt 1.5)

The probability density function of X is f(x)={{:(x, 0 lt x lt 1), (2-x, 1 le x lt 2), (0, "otherwise"):} Find P(1.2 le X lt 1.8)

If X is the random variable with porbability density function f(x) given by f(x)={(x-1,1lt=xlt2),(-x+3,2lt=xlt3),(0,"otherwise"):} find (i) the distribution function F(x) (ii) P (1.5lt=X lt=2.5)

The probability density function of random variable X is given by f(x)= {(k,1lt=xlt5),(0,"otherwise"):} Find (i) Distribution function (ii) P(X lt 3) " (iii)" P(2ltX lt4) "(iv)" P(3 lt=X)

For the probabilty density function f(x) [ {:(,cx(1-x)^(3),0 lt x lt 1),(,0,"elsewhere"):} find the constant c.

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)

A random variable X has a probability density function f(x) ={{:(,k,0 lt x lt 2pi),(,0,"elesewhere"):} find (i) k , (ii) P ( 0 lt X lt pi//2) (iii) P(pi//2 lt X lt 3pi//2)

The probability density function of X is given by f(x) = {(ke^(-x/3),"for" " "xgt0),(0, "for" " " xlt=0):} Find (i) the value of k (ii) the distribution function (iii) P(X lt 3) (iv) P(5lt=X) (v) P(X lt=4) .

Find the constant C such that the function f(x) = {(Cx^(2),1ltxlt4),(0,"Otherwise"):} is a density function and compute (i) P (1.5 lt X lt 3.5) "(ii)" P(Xlt=2) "(iii)" P (3lt X ) .