TEST 1 SOL

# TEST 1 SOL - IE 336 Fbb 23,2011 Na,me fslkr fin Test \$1 1...

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IE 336 Fbb. 23,2011 Na,me: fslkr fin --- \) Test \$1 1. Let N be a positive integer. Further, let p(a,Y): @Y'L 1n,A 1N, be the joint pdf of discrete random rrariables X and Y (the values s and g ca,a take are integers). 6 1r1 O"t t*io" the value of the constant c. \$ (b) Compute ^E(X-llr: s). { (c) Compute E(X-r). \$ (d) Comput" 'vffifi (Each of the aruIwers should be function only of N.) ^J ^J ^) 2/ caj=l il>t1-'t tt A, AJ cLxl1:l d'-r X--,t ,(ry)'=' c_(!Jy)-' l(x=rr) = !-,oJ: cn ry = (dl\$)-' ^ 3=' Lt P(Y'y) = l,rn = ,J glp : 1@rr1-', lk,n)Il"'l"l = (ry)-' ^)=c^) : ylr^,1) e (X" ly'4 = €/x-') A, = / x'' ?(N,4 1=l rl = Z^.,[9)-'u T;t : /N (r'ltrt)-' i I \ LI x--, c) Sq,r,r ar ([) €(x-,) ,ffi d) E(,Vlrt =1) t - '. ' E(V-,R 1L lru+t =g

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IE 336 Fbb. 23,201L Nnme: [stlt. In be the onestep transition matrix of the Markov chain X (rows and columns of matrix P a,re ordered in the sarne way the states are, i.e. the first row/column corresponds to state 3, the second row/column corresponds to state 5, and the third ront/column corresponds to
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## This note was uploaded on 05/05/2011 for the course IE 336 taught by Professor Bruce,s during the Spring '08 term at Purdue.

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TEST 1 SOL - IE 336 Fbb 23,2011 Na,me fslkr fin Test \$1 1...

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