Question

A radio astronomer is attempting to measure radio frequency (RF) emmisions from a certain star. However, these emissions are corrupted by a variety of independent noise sources including thermal noise in his receiving equipment, interference from local RF sources, and galactic noise. The astronomer has studied each of these sources and found them all to be well modeled as zero- mean Gaussian random variables with the following standard deviations:
T, thermal noise, σT = 5μV,
I, Interferance, σI = 2μV,
G, galactic noise, σG = 1μV.
Let represent the combined effect of all three noise sources, that is N = T + I + G. Suppose the desired emissions from the star are received at a level of 10 µV. What is the probability that the combined noise is larger than the desired emissions?

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