exercise:Ea4a38afb2: Difference between revisions
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Let <math>X_1</math>, <math>X_2</math>, | Let <math>X_1</math>, <math>X_2</math>, ..., <math>X_n</math> be an independent trials process with | ||
normal density of mean 1 and variance 2. Find the moment generating function | normal density of mean 1 and variance 2. Find the moment generating function | ||
for | for | ||
Latest revision as of 00:10, 15 June 2024
Let [math]X_1[/math], [math]X_2[/math], ..., [math]X_n[/math] be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for
- [math]X_1[/math].
- [math]S_2 = X_1 + X_2[/math].
- [math]S_n = X_1 + X_2 +\cdots+ X_n[/math].
- [math]A_n = S_n/n[/math].
- [math]S_n^* = (S_n - n\mu)/\sqrt{n\sigma^2}[/math].