GATE EC 2019 Set 1 — Question 28
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Engineering Mathematics → Probability → Expectation & Variance
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Question
If and are random variables such that and , then ________.
Correct answer
11 to 11
Solution
We are given two equations involving the expectation of random variables and . We will use the linearity property of expectation, which states that for constants .Given Equation 1:
Applying linearity of expectation:
(Equation A)Given Equation 2:
Applying linearity of expectation:
(Equation B)Let and . The system of linear equations becomes:
1)
2) From Equation (1), we can express in terms of :
Substitute this expression for into Equation (2):
Now, substitute the value of back into the expression for :
So, and .The question asks for :
.The final answer is
Applying linearity of expectation:
(Equation A)Given Equation 2:
Applying linearity of expectation:
(Equation B)Let and . The system of linear equations becomes:
1)
2) From Equation (1), we can express in terms of :
Substitute this expression for into Equation (2):
Now, substitute the value of back into the expression for :
So, and .The question asks for :
.The final answer is
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