Q20.Consider n bits X1,…,Xn, where each bit is equally likely to be 0 or 1, and is independent of all other bits. Define n−1 bits Yi=XiXi+1, i=1,…,n−1. Let NX and NY be, respectively, the number of 1s in {X1,…,Xn} and {Y1,…,Yn−1}. Assuming n=100, what is the expected value of NX and NY?
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Q20
7 Jul 2024
Q20.Consider n bits X1,…,Xn, where each bit is equally likely to be 0 or 1, and is independent of all other bits. Define n−1 bits Yi=XiXi+1, i=1,…,n−1. Let NX and NY be, respectively, the number of 1s in {X1,…,Xn} and {Y1,…,Yn−1}. Assuming n=100, what is the expected value of NX and NY?
