A uniformly distributed random variable has minimum and maximum values of 20 and 60, respectively. A) Draw the density function? B)determine P(35<x<45).

Question

 C) Draw the density function including the calculation of the probability in part B.

Answer 1

 

f(x) =     0 if x<20

  

            1/(60-20) = 1/40   if 20 <= x <= 60

 

           0 if x>60

 

The graph is a rectangle with dimensions length = 40 and width 1/40.

 

P (35 < x < 45) = integral {( 1/40) dx }  for 35<x<45

 

                         = [ (1/40)X ], 35 < x < 45

 

                         = (1/40) [ 45 - 35] =  10/40 = 1/4 = .25 = 25%

 

 

The quick a dirty way without the calculus:   (45-35)/(60-20) = 10/40 = 1/4 = .25 = 35%