Question

The probability distribution function of continuous random variable X is given by
f( x ) = `x/4`,  0 < x < 2
        = 0,       Otherwise
Find P( x ≤ 1)

Answer 1

P( x ≤ 1) = `int_0^1 f( x )` dx

              = `int_0^1 x/4` dx

              = `[ x^2/8 ]_0^1`

              = `1/8`