GATE DA 2024 Set 1 — Question 65
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Probability & Statistics → Discrete Random Variables → Covariance of RVs
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Question
Two fair coins are tossed independently. is a random variable that takes a value of 1 if both tosses are heads and 0 otherwise. is a random variable that takes a value of 1 if at least one of the tosses is heads and 0 otherwise.The value of the covariance of and is ______ (rounded off to three decimal places).
Correct answer
0.062 to 0.063
Solution
Let the sample space of tossing two fair coins be . Each outcome has a probability of .Define the random variable :
The product takes the value only if both and . Since implies (if both are heads, then at least one is heads), the condition is equivalent to (outcome ).
- if both tosses are heads (outcome ).
- otherwise (outcomes ).
- if at least one toss is heads (outcomes ).
- otherwise (outcome ).
The product takes the value only if both and . Since implies (if both are heads, then at least one is heads), the condition is equivalent to (outcome ).
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