(New page: If p1 is the probability of an echo for a single pulse when there is no object and p2 is the probability when there is an object, does that mean p2 is the probability of an echo for ONE si...)
 
 
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If p1 is the probability of an echo for a single pulse when there is no object and p2 is the probability when there is an object, does that mean p2 is the probability of an echo for ONE single pulse when there is an object?  Or is p2 a probability independent of p1?  Okay after reading this, I think that p1 is an independent probability that we tie into a max-likelihood estimation rule with p2.  So if p1 is probability of echo for 1 pulse and no object then it should be low right because echoes occur when there is an object? So is the probability of an echo for 1 pulse and there is an object 1-p1 ?  Furthermore is the probability of an echo for n pulses and no object mean p1^n and if there is an object: (1-p1)^n?  Can we now relate the two?
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If p1 is probability of echo for 1 pulse and no object then it should be low right?  Because echoes occur when there is an object. So is the probability of an echo for 1 pulse and there is an object 1-p1 ?  Furthermore is the probability of an echo for n pulses and no object mean p1^n and if there is an object: (1-p1)^n?  How can we then relate p1 and p2?
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I was looking back at the 11-05-08 lecture and noticed the coin w/ unknown bias example where Pr[H] = P in n tosses.  The ML of the probability = number of heads/n.  So can we say that ML of this probability p1 of echoes in n pulses = p1/n?

Latest revision as of 18:42, 10 November 2008

If p1 is probability of echo for 1 pulse and no object then it should be low right? Because echoes occur when there is an object. So is the probability of an echo for 1 pulse and there is an object 1-p1 ? Furthermore is the probability of an echo for n pulses and no object mean p1^n and if there is an object: (1-p1)^n? How can we then relate p1 and p2?

I was looking back at the 11-05-08 lecture and noticed the coin w/ unknown bias example where Pr[H] = P in n tosses. The ML of the probability = number of heads/n. So can we say that ML of this probability p1 of echoes in n pulses = p1/n?

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Sean Hu, ECE PhD 2009