Question

Write a program to choose a random number X in the interval [2,10] 1000 times and record what fraction of the outcomes satisfy X > 5, what fraction satisfy 5 < X < 7, and what fraction satisfy x2 −12x+35 > 0. How do these results compare with Exercise 1?

Answer 1

Since is chosen randomly from the interval, no area of the interval is more likely to be drawn from than any other. The density function for the outcome of is uniform (constant).

The cumulative distribution function, , is:

where

   where

  where   

The probability density function, , is the derivative of the cumulative distribution function:

   where   

   where   

     where   

And the probability of some event occurring where is a sub interval of is

For,

For,

  

And For,

  

Thus, the program is

Experimental results from drawing a random real number from times: