Consider a bitstring of length 5. in which each bit is 0 with probability 1/2 (a

Question

Consider a bitstring of length 5. in which each bit is 0 with probability 1/2 (and, thus, 1 with probability 1/2), independently of the other bits. Define the random variables X and Y as follows: X = the number of Os in this bitstring and Y = the value of the first bit in this bitstring. Which of the following is true? The random variables X and Y are independent. The random variables X and Y are not independent. None of the above. One of Lindsay and Simon is chosen uniformly at random. The person that is chosen wins $100. Define the random variables L and S as follows: L = the amount that Lindsay wins and S = the amount that Simon wins. Which of the following is true? E(L) = 50 and E(max(L, S)) = 50. E(L) = 100 and E(max(L,S)) = 100. E(L) = 50 and E(max(L, S)) = 100. E(L) = 100 and E(max(L, S)) = 50.

Explanation / Answer

1) ANS:

b) the random variables X and Y are not independent.

why because, here X denotes the no of 0s in bitstring. here Y denotes the value of first bit in the bitstring so if it is 1, then the value of X decreases. if it is 0 then the value of X increases so obviously X value depends on Y value, so the random variables X and Y are not independent.

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