GATE EE 2025 Set 1 — Question 15
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Engineering Mathematics → Probability → Conditional Probability
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Question
Consider discrete random variables and with probabilities as follows:Given , the expected value of is
Correct answer
(B) (1)/(2)
Solution
The expected value of given is defined as:First, we find the marginal probability :
Next, we find the conditional probabilities :
Now, calculate the expected value:
E[Y | X = 1] = 0 \cdot \left(\frac{1}{2}\right) + 1 \cdot \left(\frac{1}{2} ight) = \frac{1}{2}Thus, the expected value of given is .
Next, we find the conditional probabilities :
Now, calculate the expected value:
E[Y | X = 1] = 0 \cdot \left(\frac{1}{2}\right) + 1 \cdot \left(\frac{1}{2} ight) = \frac{1}{2}Thus, the expected value of given is .
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