Moment Generating Functions
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Can you please explain me how I can use the moment generating functions to find the limiting distribution:
Suppose that Zi for N(0,1) and that Z1, Z2,...are independent. Use moment generating functions to find the limiting distribution of... (see attached file).
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This solution explains moment generating functions to help calculate the limiting distribution of the function mentioned.
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7.5 Suppose that and that are independent. Use moment generating functions to find the limiting distribution of .
PLEASE: can you explain me about how I use the moment generating functions to find the limiting distribution
First, we want to recall what the moment generating function is.
For a random variable X, the moment generating function with respect to X is
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Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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