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Questions › JNU › JNU SSS 2012 › Q13
1 mark, −0.25Statistics › Random variables and standard distributions › Expectation and varianceModerateabout 1 min

JNU SSS 2012 Question 13: Random variables and standard distributions

A random variable YYY has the following distribution :

YYY−1-1−1012
P(Y)P(Y)P(Y)3C3C3C2C2C2C0·40·1

Consider the random variable 2×Y+r22 \times Y + r^22×Y+r2, where rrr is a real number. The mean of this random variable is 0·7. Which of the following must be true?

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Plain-text version

A random variable Y has the following distribution: | Y | -1 | 0 | 1 | 2 | P(Y) | 3C | 2C | 0·4 | 0·1 | Consider the random variable 2 × Y + r², where r is a real number. The mean of this random variable is 0·7. Which of the following must be true? (A) r = 0·10 (B) r = 0·05 (C) r² = 0·40 (D) None of the above

Also written as: A random variable Y has the following distribution: | Y | -1 | 0 | 1 | 2 | P(Y) | 3C | 2C | 0·4 | 0·1 | Consider the random variable 2 * Y + r^2, where r is a real number. The mean of this random variable is 0·7. Which of the following must be true?

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 JNU SSS 2012 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.