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mt1-sample-solutions

# mt1-sample-solutions - Y = you understand F = f riend...

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Y = you understand F = friend understands P ( Y ) = 0 . 5 P ( F ) = 0 . 6 P ( Y F ) = 0 . 25 P ( Y ) P ( F ) = 0 . 5 × 0 . 6 = 0 . 3 = 0 . 25 P ( Y ) P ( F ) = P ( Y F ) P ( Y C F ) P ( F ) = P ( Y F ) + P ( Y C F ) 0 . 6 = 0 . 25 + P ( Y C F ) 0 . 35 = P ( Y C F )

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S = taking steroids T = tests positive for steroids P ( T | S ) = 0 . 80 P ( T C | S C ) = 0 . 95 P ( S ) = 0 . 10 P ( S | T ) P ( S | T ) = P ( S ) P ( T | S ) P ( T ) = P ( S ) P ( T | S ) P ( T S ) + P ( T S C ) = P ( S ) P ( T | S ) P ( S ) P ( T | S ) + P ( S C ) P ( T | S C ) = 0 . 10(0 . 80) 0 . 10(0 . 80) + 0 . 90(0 . 05) = 0 . 08 0 . 08 + 0 . 045 = 0 . 64
μ = np = 10 × 1 6 = 1 . 667 σ 2 = np (1 p ) = 10 × 1 6 × 5 6 = 1 . 389 P ( X > 0) P ( X > 0) = 1 P ( X = 0) = 1 10 0 ( 1 6 ) 0 ( 5 6 ) 10 = 1 0 . 162 = 0 . 838

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X P ( X < 10) = 0 . 5 P ( X < 5) = P ( Z < 5 10 2 ) = P ( Z < 2 . 5) = 0 . 0062 P ( X > 12) = P ( Z > 12 10 2 ) = P ( Z > 1) = 0 . 1586 P (7 < X < 13) = P ( 7 10 2 < Z < 13 10 2 ) = P ( 1 . 5 < Z < 1 . 5) = 1 2(0 . 0668) = 0 . 8664 P ( X < 6 X > 14) = P ( Z < 6 10 2 Z > 14 10 2 ) = P ( Z < 2 Z > 2) = 2(0 . 0228) = 0 . 0455 x P ( X < x ) = 0 . 95 Z P ( Z < z ) = 0 . 95 z = 1 .
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mt1-sample-solutions - Y = you understand F = f riend...

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