Statistics...Uniform distribution?

A random number generator is used to generate a real number at random between 0 and 1, equally likely to fall anywhere in this interval of values. (For instance, 0.3794259832...is a possible outcome.)





a. Sketch a curve of the probability distribution of this random variable, which is the continuous version of the uniform distribution.





b. What is the mean of this probability distribution?





c. Find the probability that this random variable falls between 0.25 and 0.75.





*Note:


The mean of a probability distribution for a discrete random variable is





µ = Σ x P(x)





where the sum is taken over all possible values of x.

Statistics...Uniform distribution?
f(x)=1, 0 %26lt; x %26lt; 1 is the probability density function of the random variable x.


More generally, it is f(x)=1/(b-a) a %26lt; x %26lt; b; Here b=1 and a=0.


The source shows a sketch.


b) mean = integral (0 to 1) xdx


=x^2/2 (0 to 1)


1/2


c)integral( 0.25 to 0.75) dx


=x (between limits 0.25 and 0.75)


=0.75-0.25=0.50
Reply:f(x)=1, 0 %26lt; x %26lt; 1 is the probability density function of the random variable x.


More generally, it is f(x)=1/(b-a) a %26lt; x %26lt; b; Here b=1 and a=0.


The source shows a sketch.


b) mean = integral (0 to 1) xdx


=x^2/2 (0 to 1)


1/2


c)integral( 0.25 to 0.75) dx


=x (between limits 0.25 and 0.75)


=0.75-0.25=0.50


Here, we are dealing with a continuous (not discrete) random variable.