Given the pdf fx 4x3 0 SolutionAnswer Given Probability Den

Solution

Answer

Given Probability Density Function is

f (x) = { (4 x³ ), 0 < x < 1 ; 0 , elsewhere}

Calculating p (x 1/3 ) = [ 4 * x⁴ / 4 ] limit 0 to 1/3

                                          = [ (1/3)⁴ - (0)⁴ ]

                                          = 0.01234     

And, p (x > 7/8 ) = [ 4 * x⁴ / 4 ] limit 7/8 to 1

                                          = [ (1)⁴ - (7/8)⁴ ] = 1 – 0.5818

                                          = 0.4138

So, p [ (x 1/3) U (x > 7/8)] = (0.01234 + 0.4138)

                                           = 0.4261