lec3 (1)

lec3 (1) - (R|) = cos + sin = 2 1/2 cos( - /4) 2. Identify...

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(R| Ψ ) = cos Ψ + sin Ψ = 2 1/2 cos( Ψ - π /4) 2. Identify Sample Space 3. Probability Law over Sample Space: Invoke isotropy implying uniformity of angle 0 π /2 ψ
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0 π /2 ψ 2 / π f Ψ ( ψ )
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4. Find CDF ± F R (r) = P{R < r} = P{2 1/2 cos( Ψ - π /4) < r} ± F R (r) = P{R < r} = P{cos( Ψ - π /4) < r/ 2 1/2 }
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1 r/2 1/2 1/2 1/2 0 π /2 π /4 cos( Ψ - π /4) Ψ g( Ψ )
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1 r/2 1/2 1/2 1/2 0 π /2 π /4 cos -1 (r/2 1/2 ) + π /4 -cos -1 (r/2 1/2 ) + π /4 cos( Ψ - π /4) Ψ g( Ψ )
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2/ π 1 0 π /2 π /4 cos -1 (r/2 1/2 ) + π /4 -cos -1 (r/2 1/2 ) + π /4 Ψ pdf for Ψ Probability of 'red event' = 2*(2/ π )*{-cos -1 (r/2 1/2 ) + π /4}
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And finally. .. ± After all the computing is done, we find: ± F R (r) = 1 - (4/ π )cos -1 (r/2 1/2 ), 1< r <2 1/2 ± f R (r) = d[F R (r) ]/dr = (4/ π ) {1/(2 - r 2 ) 1/2 } ± Median R = 1.306 ± E[R] = 4/ π = 1.273 ± σ R /E[R] = 0.098, implies very robust
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A Quantization Problem
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Marine Transfer Station Loading Barge Loading Barge Loading Barge Loading Barge
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This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.

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lec3 (1) - (R|) = cos + sin = 2 1/2 cos( - /4) 2. Identify...

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