# What is the height of the density curve between 0 and 2? Draw a graph of the density curve.Many random-number generators allow users to specify the range of the random numbers to be produced....

What is the height of the density curve between 0 and 2? Draw a graph of the density curve.

Many random-number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the range is to be all numbers between 0 and 2. The density curve for the outcome has constant height between 0 and 2, and height 0 elsewhere.

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### 1 Answer

The density function is defined like this case could be defined like probability of getting any number in the domain (0<=x<=2) is the same.

Let f(x) = k .................(1), be the density function, for o<=x<=2

Then f(x) = 0 for any other x .

Then for a density function, Integral f(x) dx should be 1 for x fro x=0 to x=2. Or

{Integral kdx from x=0 to x=2} should equal to 1.Or

{[(kx)atx=2]- [(kx) at x=0} should be equal to 1. Or

2k-0 =1 . Or

k = 1/2. Substitute this value of k in (1) .

Therefore, the uniform height of the curve (or ordinate of the curve) is f(x) = k Or f(x) = 1/2. Or y =f(x) =** 1/2.**