Timeline for What is $E(e^{rX^2})$ when $X~N(0,\sigma^2)$? [duplicate]
Current License: CC BY-SA 4.0
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| Apr 28, 2021 at 22:09 | review | Reopen votes | |||
| Apr 28, 2021 at 22:12 | |||||
| Apr 28, 2021 at 21:47 | comment | added | roundsquare | Ah, gotcha. I did not realize that was the definition of chi-squared. I'm not sure if it matters that the r.v. $X$ is not standard normal since the variance is not $1$. But I think I am confident that my formula is correct now. Thanks! Sadly, this means I'm stuck at the next step instead :( | |
| Apr 28, 2021 at 21:44 | history | edited | roundsquare | CC BY-SA 4.0 |
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| Apr 28, 2021 at 14:20 | comment | added | whuber♦ | Yes: by definition, the sum of squares of independent standard Normal variables has a chi-squared distribution. You are computing the mgf of the square of a single variable that is a multiple of a standard Normal. | |
| Apr 27, 2021 at 22:34 | comment | added | roundsquare | @whuber I'm not seeing the connection to chi-squared distributions. Here, $X$ has a normal distribution. Am I missing something? | |
| Apr 27, 2021 at 20:52 | history | duplicates list edited | whuber♦ | duplicates list edited from Pdf of the square of a general normal random variable to Finding the Moment Generating Function of chi-squared distribution, Pdf of the square of a general normal random variable, What is the moment generating function of the generalized (multivariate) chi-square distribution?, Distributions of Quadratic form of a normal random variable | |
| Apr 27, 2021 at 20:49 | history | closed | whuber♦ | Duplicate of Pdf of the square of a general normal random variable | |
| Apr 27, 2021 at 20:48 | comment | added | whuber♦ | You are computing the moment generating function of a multiple of a chi-squared distribution. The details can be found in several threads here. | |
| Apr 27, 2021 at 20:40 | history | asked | roundsquare | CC BY-SA 4.0 |