Question: 2015 Winter Final - 21

Author: Michiel Smid

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 0s in this bitstring

and

Y = the value of the first bit in this bitstring.

Which of the following is true?

(a)

The random variables $X$ and $Y$ are independent.

(b)

The random variables $X$ and $Y$ are not independent.

(c)

None of the above.