Fundamentals of Probability and Statistics for Engineers

236 Fundamentals of Probability and Statistics for EngineersTable 7.1 Summary of continuous distributionsDistribution Probability density function Parameters Mean and varianceUniform f X x) ˆ 1b a , a x b a, b > a a ‡ b2,b a)212Normal Gaussian) f X x) ˆ1x m) 2 2) 1/2 exp 2 2,m, >0 m, 2Lognormal f Y y) ˆ1 < x < 1 ln 2 yY1yln Y2) 1/2 exp 12 2 ln Y, y 0 Y > 0, ln Y > 0 Y exp 2 ln Y2, m 2 Y [ exp 2 ln Y ) 1]Gamma f X x) ˆ ) x 1 exp x), x 0 >0, >0 , 2Exponential f X x) ˆ exp x), x 0 >01 , 1 2Chi-squared f X x) ˆ12 /2 /2) x/2) 1 exp x/2), ˆ positive integer , 2x 0TLFeBOOK