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Questions › DSE › DSE 2020 › Q2
4 marks, −1Statistics › Random variables and standard distributions › Expectation and varianceModerateabout 3 min

DSE 2020 Question 2: Random variables and standard distributions

A coin has outcomes HHH and TTT with probabilities 3/43/43/4 and 1/41/41/4. A gambler tosses until the first HHH. If the first HHH occurs on the nnn-th toss and nnn is odd, the prize is −2n-2^n−2n; if nnn is even, the prize is 2n2^n2n. The expected value of the prize is

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A coin has outcomes H and T with probabilities 3/4 and 1/4. A gambler tosses until the first H. If the first H occurs on the n -th toss and n is odd, the prize is -2ⁿ; if n is even, the prize is 2ⁿ. The expected value of the prize is (A) 1 (B) -1 (C) 3 (D) -3

Also written as: A coin has outcomes H and T with probabilities 3/4 and 1/4. A gambler tosses until the first H. If the first H occurs on the n -th toss and n is odd, the prize is -2^n; if n is even, the prize is 2^n. The expected value of the prize is

Random variables and standard distributions has come up 173 times in 7 exams since 2005.

What this question tests

This question is on Expectation and variance, part of Random variables and standard distributions in Statistics.

The mean and spread of a random variable, and how they change under transformations and sums.

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Question from the DSE 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.