# lec6 - MIT OpenCourseWare http/ocw.mit.edu 8.044...

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MIT OpenCourseWare http://ocw.mit.edu 8.044 Statistical Physics I Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Example Random number generator for programmers p(x) p(y) 1 1 0 1 x 0 1 y x and y are statistically independent 8.044 L6B1
z MAX( x, y ) Find p ( z ) p ( x, y )= p ( x ) p ( y ) Where is MAX( x, y η ? Where is MAX( x, y ) ? A 01 x 1 y η η p(x,y)=1 p(x,y)=0 8.044 L6B2

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± ± p(z) B P z ( η )= η 2 2 C p z ( η )=2 η 0 η 1 0 1 z 1 <z > = 2 η 2 =(2 / 3) [ 1 0 η 3 =2 / 3 0 2 1 0 η 4 =1 / 2 > = 2 η 3 / 4) [ 1 0 1 Var( z )= 1 4 = 1 S.D. = 18 =0 . 24 2 9 18 , 8.044 L6B3
v Example Desorbing atom p ( v, θ, φ )= p ( v ) p ( θ ) p ( φ ) p ( v )=(1 / 2 σ 4 ) v 3 exp[ v 2 / 2 σ 2 ] p ( θ )=2 sin θ cos θ p ( φ )=1 / 2 π Find p ( v z ) z x y n θ φ leaving the surface 8.044 L6B4

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A v z = v cos θ v v cos θ<γ v<γ/ cos θ γ θ π /2 8.044 L6B5
± ± ² ± C B π/

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lec6 - MIT OpenCourseWare http/ocw.mit.edu 8.044...

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