GATE CS 2015 Set 3 — Question 61
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Engineering Mathematics → Probability & Statistics → Conditional Probability
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Question
Suppose for are independent and identically distributed random variables whose probability mass functions are for . Define another random variable , where denotes XOR. Then __________.
Correct answer
0.75 to 0.75
Solution
We need to find .Given , the expression for becomes:
Since , we have .We want to find the probability that , i.e., .The product is 0 if either or (or both). It is 1 only if both and .Since are independent Bernoulli(0.5) variables:
.Therefore,
.
Since , we have .We want to find the probability that , i.e., .The product is 0 if either or (or both). It is 1 only if both and .Since are independent Bernoulli(0.5) variables:
.Therefore,
.
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