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Unformatted text preview: is the n th real root o² t = g ( θ ) and g ′ ( θ ) = dg ( θ ) dθ . We consider two possible regions o² t values: • When | t | > d/c , the ²unction t = ( d/c ) cos( θ ) has no solutions; hence f T ( t ) = 0. • When | t | < d/c , and-π < θ < π , the ²unction t = ( d/c ) cos( θ ) has two solutions, θ 1 = arccos( c t/d ) , θ 2 = 2 π-arccos( c t/d ) . (2) The derivative o² g ( θ ) is given by g ′ ( θ ) = (-d/c ) sin( θ ). So, using (2), the denominator o² (1) becomes | g ′ ( θ n ) | = r ( d/c ) 2-T 2 , n = 1 , 2. Also, f Θ ( θ ) = 1 / 2 π within-π to π . Thus, (1) becomes f T ( t ) = 2 2 π r ( d/c ) 2-t 2 , | t | < d/c. The resulting probability density ²unction o² T is given by: f T ( t ) = 2 2 π r ( d/c ) 2-t 2 , | t | < d/c , | t | > d/c 1...
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This note was uploaded on 01/26/2011 for the course EEE 554 taught by Professor Duman during the Spring '10 term at ASU.
- Spring '10