Page 146 - Schaum's Outlines - Probability, Random Variables And Random Processes
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CHAP. 41 FUNCTIONS OF RANDOM VARIABLES, EXPECTATION, LIMIT THEOREMS 139
Fig. 4-7
which is sketched in Fig. 4-7(c). Note that the same result can be obtained by the convolution of fAz) and
fd4.
4.20. Let X and Y be independent gamma r.v.'s with respective parameters (a, A) and (j?, A). Show that
Z = X + Y is also a gamma r.v. with parameters (a + #3, A).
From Eq. (2.76) (Prob. 2.24),
The range of Z is (0, co), and using Eq. (4.80a), we have
By the change of variable w = x/z, we have
