Question

In: Statistics and Probability

Write a program to choose a random number X in the interval [2,10] 1000 times and...

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?

Expert Solution

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

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

where

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

For,

And For,

Thus, the program is

Experimental results from drawing a random real number from times:

orchestra answered 2 years ago

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