# Question: A radio astronomer is attempting to measure radio frequency RF

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?

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?

**View Solution:**## Answer to relevant Questions

A certain system we have designed needs to be powered by a 24- V dc supply. Available to us in our lab are each of the following types of batteries whose statistical characteristics (and quantities available) are as shown in ...Consider a vector of random variables, X = [X1, X2. XN] T. Suppose we form a new random variable Z by performing a weighted average of the components of X. That is, Where Find the values of the constants bi such that the ...Let Xn be a sequence of IID Gaussian random variables. Form a new sequence according to Determine which forms of convergence apply to the random sequence. Let, Xk k = 1, 2, 3… be a sequence of IID Cauchy random variables with and let Sn be the sequence of sample means, (a) Show that also follows a Cauchy distribution. (b) Prove that in this case, the sample mean does not ...A company manufactures five- volt power supplies. However, since there are manufacturing tolerances, there are variations in the voltage design. The standard deviation in the design voltage is 5%. Using a 99% confidence ...Post your question