The probability mass function of a random variable X is given by P(X=n)=2^-n; quad n=1,2,3,… Define a random variable Y=begincases-1, & if X is odd+1, & if X is evenendcases With reference to the above, consider the following statements: I. P(Y=1)=2/3 II. E(Y)=-1/3 III. V(Y)=8/9 Which of the statements given above are correct?

Q34Section I (Objective (Q1–Q80))34 of 79

Distribution Theory — moments of a parity-based sign transform

The probability mass function of a random variable $X$ is given by

$P(X=n)=2^{-n}; \quad n=1,2,3,…$

Define a random variable

$Y=\begin{cases}-1, & \text{if } X \text{ is odd}\\+1, & \text{if } X \text{ is even}\end{cases}$

With reference to the above, consider the following statements:

$\text{I. } P(Y=1)=2/3$

$\text{II. } E(Y)=-1/3$

$\text{III. } V(Y)=8/9$

Which of the statements given above are correct?

Pick an option to check your answer. In a mock test a wrong answer here costs 0.83 mark.

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