A random variable X takes only nonzero integer values from to , with a probability mass function symmetric around 0. Consider . Which of the following is an appropriate definition for , the probability mass function of Y?
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A random variable X takes only nonzero integer values from -20 to +20, with a probability mass function f(x) symmetric around 0. Consider Y=X². Which of the following is an appropriate definition for g(y), the probability mass function of Y? (A) g(y)=f(√y) for y=1,4,…,400 and 0 otherwise. (B) g(y)=[f(√y)]² for y=1,4,…,400 and 0 otherwise. (C) g(y)=2f(√y) for y=1,4,…,400 and 0 otherwise. (D) g(y)=√(f(√y)) for y=1,4,…,400 and 0 otherwise.
Also written as: A random variable X takes only nonzero integer values from -20 to +20, with a probability mass function f(x) symmetric around 0. Consider Y=X^2. Which of the following is an appropriate definition for g(y), the probability mass function of Y?
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This question is on Transformations and order statistics, part of Random variables and standard distributions in Statistics.
The distribution of a function of a random variable, and of the largest or smallest of several.
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