Thread: A PROBLEM in continuous random variable

A radar sends out 2000 pulses of a particular shape and listens for the return signal of each of these pulses. The radar receiver listens for bursts of pulses and declares a target if it detects k or more pulses in a short time interval. Through tests, the value of k is adjusted in the radar receiver until the probability of target declaration exeeds 0.95. Energy absorbing "paint" is then applied to the target. This material has the property that each millimeter of thickness reduces the radar receiver's probability of detecting a single pulse by 10%. How thick does the coating have to be to reduce our radar's probability of detection to 0.50 or smaller??

Originally Posted by gravity2910

A radar sends out 2000 pulses of a particular shape and listens for the return signal of each of these pulses. The radar receiver listens for bursts of pulses and declares a target if it detects k or more pulses in a short time interval. Through tests, the value of k is adjusted in the radar receiver until the probability of target declaration exeeds 0.95. Energy absorbing "paint" is then applied to the target. This material has the property that each millimeter of thickness reduces the radar receiver's probability of detecting a single pulse by 10%. How thick does the coating have to be to reduce our radar's probability of detection to 0.50 or smaller??

That is incoprehensible, are those the exact words of the problem?

CB

I copied exactly from my homework set. Actually, I can compute the value of k, which is 103 pulses. But I've got some confusion about the rest of the problem.

Originally Posted by gravity2910

I copied exactly from my homework set. Actually, I can compute the value of k, which is 103 pulses. But I've got some confusion about the rest of the problem.

Can you tell us how you compute that?

CB

P[X>=k]=0.95= 1-F(k)=1-1+e^(-lamda*k) where lamda=1/2000.
=>k=103
(I approximately assume the density is exponential distributed density function.)

Originally Posted by gravity2910

P[X>=k]=0.95= 1-F(k)=1-1+e^(-lamda*k) where lamda=1/2000.
=>k=103
(I approximately assume the density is exponential distributed density function.)

I don't see where any of that comes from your question as asked. For instance how is your short period of time related to the 2000 pulses, it looks like you may have an n from m detector in mind with n=k and m=2000, but that is not what your question asks.

All of which suggests there is more information behind thia question whithout which we cannot help.

CB