Question 8674 – GATE 2014 [Set-3]
December 31, 2023GATE 1999
December 31, 2023GATE 1999
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Question 1
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Suppose that the expectation of a random variable X is 5. Which of the following statements is true?
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There is a sample point at which X has the value 5.
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There is a sample point at which X has value greater than 5.
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There is a sample point at which X has a value greater than or equal to 5.
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None of the above
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Question 1 Explanation:
Expectation of discrete random variable
E(X) = x1P1 + x2P2 + … + xnPn
In question, E(X) is given as 5.
E(X) = 5, 0≤Pi≤1
P1 + P2 + … + Pn = 1 [Probability]
Therefore, E(X) = 5 is possible only if atleast one of the xi value is greater than 5.
E(X) = x1P1 + x2P2 + … + xnPn
In question, E(X) is given as 5.
E(X) = 5, 0≤Pi≤1
P1 + P2 + … + Pn = 1 [Probability]
Therefore, E(X) = 5 is possible only if atleast one of the xi value is greater than 5.
Correct Answer: C
Question 1 Explanation:
Expectation of discrete random variable
E(X) = x1P1 + x2P2 + … + xnPn
In question, E(X) is given as 5.
E(X) = 5, 0≤Pi≤1
P1 + P2 + … + Pn = 1 [Probability]
Therefore, E(X) = 5 is possible only if atleast one of the xi value is greater than 5.
E(X) = x1P1 + x2P2 + … + xnPn
In question, E(X) is given as 5.
E(X) = 5, 0≤Pi≤1
P1 + P2 + … + Pn = 1 [Probability]
Therefore, E(X) = 5 is possible only if atleast one of the xi value is greater than 5.