GATE EC 2025 Set 1 — Question 58
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Engineering Mathematics → Probability → Expectation & Variance
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Question
Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable denote the sum of the outcomes obtained.
The expectation of is
(rounded off to two decimal places).
The expectation of is
(rounded off to two decimal places).
Correct answer
6.95 to 7.05
Solution
Let be the outcome of the first die and be the outcome of the second die.
Each die is fair, so the probability of rolling any number from 1 to 6 is .The expectation of a single fair die roll is:
The random variable denotes the sum of the outcomes obtained, so .
By the linearity of expectation, the expectation of the sum of random variables is the sum of their expectations:
Rounding off to two decimal places, the expectation of is .
Each die is fair, so the probability of rolling any number from 1 to 6 is .The expectation of a single fair die roll is:
The random variable denotes the sum of the outcomes obtained, so .
By the linearity of expectation, the expectation of the sum of random variables is the sum of their expectations:
Rounding off to two decimal places, the expectation of is .
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