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Assume X and. Y are. 2. independent variables that follow the standard uniform distribution i.e. U(0,1)...

Assume X and. Y are. 2. independent variables that follow the standard uniform distribution i.e. U(0,1)

Let Z = X + Y

Find the PDF of Z, fZ(z) by first obtaining the CDF FZ(z) using the following steps:

(a) Draw an x-y axis plot, and sketch on this plot the lines z=0.5, z=1, and z=1.5 (remembering z=x+y)

(b) Use this plot to obtain the function which describes the area below the lines for z = x + y in terms of z, using geometry. This CDF FZ(z) = P(Z < z). You should notice a change in the function at z=1

(c) Obtain the PDF from FZ(z)

(d) Describe the shape of the distribution of Z

Math   Statistics-And-Probability   
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(a)

(b)

(d) Shape of the distribution is triangular so it is called triangular distribution.

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