A continuous random variable X has the following density function:

a. Draw a graph of this density. Verify that the area under the density function equals 1.
b. A density function such as this one is called a uniform density, or sometimes a rectangular density. It is extremely easy to work with because probabilities for intervals can be found as areas of rectangles. For example, find PU (X ‰¤ 4.5 | Min = 3; Max = 5). (The parameters Min and Max are used to denote the lower and upper extremes, respectively.)
c. Find the following uniform probabilities:

d. Plot the CDF for the uniform distribution where Min = 0and Max = 1.
e. The expected value of a uniform distribution is E (X Þ = (Min + Max) = 2, and the variance is Var (X) = (Max €“ Min) 2 = 12. Calculate the expected value and variance of the uniform density with Min = 3; Max = 5.

Transcribed Image Text:

fix,-(0.5, others. 5 f(x)- 0. otherwise PU(X < 4.3 Min = 3, Max = 5) Pr(X>3.4 Min=0, Max= 10) PU (0.25 < X < 0.75 | Min = 0. Max= 1 ) PU (X 0 Min =-1, Max = 4)