Homework-1-solution

# Homework-1-solution - IOE 515 Stochastic Processes Homework...

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IOE 515: Stochastic Processes Homework 1 – solutions A Problem 1 (a) Denoting R =red, G = green, and B = blue, an outcome of the experiment is a pair ( i,j ) where i,j ∈ { R,G,B } and i and j denote the color of the ﬁrst and second marble, respectively. The sample space is therefore S = { ( i,j ) : i,j ∈ { R,G,B }} = { ( R,R ) , ( R,G ) , ( R,B ) , ( G,R ) , ( G,G ) , ( G,B ) , ( B,R ) , ( B,G ) , ( B,B ) } . Moreover, each of the 9 outcomes has a probability of 1 3 × 1 3 = 1 9 of occurring. (b) Again denoting R =red, G = green, and B = blue, an outcome of the modiﬁed experiment is a pair ( i,j ) where i 6 = j ∈ { R,G,B } and i and j denote the color of the ﬁrst and second marble, respectively. The sample space is therefore S 0 = { ( i,j ) : i 6 = j ∈ { R,G,B }} = { ( R,G ) , ( R,B ) , ( G,R ) , ( G,B ) , ( B,R ) , ( B,G ) } . Moreover, each of the 6 outcomes has a probability of 1 3 × 1 2 = 1 6 of occurring. Problem 2 Denote H = heads and T = tails, and let c i ∈ { H,T } be the result of the i th coin toss. (a) The sample space

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Homework-1-solution - IOE 515 Stochastic Processes Homework...

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