7.2 Sample values of Gaussian random variables Let Z be a Rayleigh random
varible (cf. Chapter 3, Example 3) with pdf
![]() a. Show that a sample value, z, of A can be obtained by setting ![]() where r, as usual, denotes a random number (0 ![]() ![]()
In Chapter 3, Example 3, it was shown that if S and Tare independent
Gaussian random variables with zero mean and standard deviation equal to
![]() then the random variable Z = ![]() ![]()
b. Using this fact and the result of part (a), show that if X and Y
are independent Gaussian random variables with mean mx and my,
respectively, and equal standard deviations, ![]() where r1 and r2 are independent random numbers in the interval [0, 1]. This result has already been quoted [cf. expressions (7.13)-(7.15)]. Hint: Review carefully Example 3 of Chapter 3.
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