# Thread: Using MGFs to deduce the PDF

1. ## Using MGFs to deduce the PDF

Suppose that $\displaystyle Y_1,Y_2,...,Y_n$ are a random sample from a normal distribution with mean $\displaystyle \mu$ and variance $\displaystyle \sigma^2$. Use MGFs to deduce the PDF of $\displaystyle \bar{Y}$.

2. Originally Posted by chella182
Suppose that $\displaystyle Y_1,Y_2,...,Y_n$ are a random sample from a normal distribution with mean $\displaystyle \mu$ and variance $\displaystyle \sigma^2$. Use MGFs to deduce the PDF of $\displaystyle \bar{Y}$.
Are $\displaystyle Y_1,Y_2,...,Y_n$ independent? Read this: Moment-generating function - Wikipedia, the free encyclopedia (Sum of independent random variables).

3. Yeah I know that, but it doesn't say in the question that they're independent

4. Originally Posted by Wikipedia
Random sampling can also refer to taking a number of independent observations from the same probability distribution, without involving any real population.
I think they introduced a sample this way in my stats course

5. Originally Posted by chella182
Suppose that $\displaystyle Y_1,Y_2,...,Y_n$ are a random sample from a normal distribution with mean $\displaystyle \mu$ and variance $\displaystyle \sigma^2$. Use MGFs to deduce the PDF of $\displaystyle \bar{Y}$.
Asked here first: http://www.mathhelpforum.com/math-he...ution-mgf.html

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