A continuous random variable x has the p.d.f defined by f(x) = `{(Ce""^(-ax),0ltxltoo),(0,"elsewhere"):}` find the value of C if `a gt 0.`

Find the mean and variance of the distribution f(x) = {(3e""^(-3x),0lt xltoo),(0,"elsewhere"):}

If X is a continuous random variable then P(X ge a)= _________.

If a random variable X has the p.d.f. f(x)=k/(x^(2)+1), 0 lt x lt infty , then k is

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

If a continuous random variable X has the p.d.f. f(x)=4k(x-1)^(3) 1<=x<=3 , then find P(1 le X le 2) .

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)

If f(x) = {(kx^(2),0ltxlt 3),(0,"elsewhere"):} is a probability density function then the value of k is ……. .

The probability density function of a random variable x is f(x) = {(kx^(alpha-1)e^(-betax^alpha),x","alpha","beta","gt0),(0,"elsewhere"):} Find (i) k, (ii) P (X gt 10) .

The time to failure in thousands of hours of an electronic equipment used in a manufactured computer has the density function f(x)={{:(3e^(-3x), x gt 0), (0, "elsewhere"):} Find the expected life of this electronic equipment.