Final answer:
To find the value of Z in a Gaussian noise channel when Y is equal to 4, and assuming the mean of X is used in the calculation, we subtract the mean of X (which is 5) from Y, yielding Z = -1.
Step-by-step explanation:
The question asks to find the value of the noise Z in a Gaussian noise channel when the output Y is given as 4. This is a mathematical problem involving normal distributions, and the relationship Y = X + Z is used, with X and Z being random variables.
The distributions of X and Y are given as X~ N(5, 6) and Y~ N(2, 1), respectively. The value of the variable Z can be found by rearranging the given equation to Z = Y - X. If Y is 4 and considering the pre-established information that X is 17 when Z is 2, we don't have enough consistent information to solve for Z because the distribution of X is at odds with X being 17 (since its mean is 5). Assuming there might be a typographical error in the question, to calculate the value of Z correctly, we would subtract the mean of X from the given Y value. Hence, Z = 4 - 5 = -1, assuming we use the mean of X for the calculation.