qnorm

• used to find normal percentiles
• input is percentile, output is the score
• qnorm(percent, mean, sd)

Sampling from a Normal Distribution

sample = rnorm(1000, mean=mu, sd=sigma)

sample[1:10] is used to get the first 10 random samples then

1,000,000 samples

1000 samples

Summing Normals

With mutually independent $X_i \sim Normal(\mu_i, \sigma_i^2)$

$Y= \sum X_i ~ Normal \space (\mu_Y = \sum \mu_i, \space \sigma_Y^2 = \sum \sigma_i^2)$

• in essence,
  • the mean is the sum of the means
  • the sd is the sqrt of the sum of the squares of the means

Q-Q Plots

• qqnorm() yields this; if normal should look like a straight line with slope 1
• qqplot() lets you compare two samples to see if they came from the same distr.
• qqline() produce a similar output
• normal distribution
• uniform distribution
• exponential distribution
• beta distribution