1/17/2024

Continue estimation activity

Moment generating function (m.g.f.)

• Find the m.g.f. of a standard normal random variable Z
• If Z is a standard normal random variable, find the distribution of X = mu + sigma*Z.
• Use the m.g.f. to show that a linear transformation of a normal random variable will also have a normal distribution.
• Use the m.g.f. to show that the sum of independent normal random variables will also have a normal distribution

Simulation

• Simulate the distributions of the mean and median for Normal data.
• Simulate the distributions of the mean and median for Cauchy data.
• Simulate the distributions of the standard deviation and the range.

We will have our first problem session on Friday.