STA220H1 Lecture Notes - Lecture 8: Probability Distribution, Normal Distribution, Standard Deviation

• School: UTSG
• Department: Statistical Sciences
• Course: STA220H1
• Professor: Shivon Sue-Chee

Document Summary

Continuous probability distributions: probability density function, continuous uniform, normal. Expectation (expected value/mean) and variance (standard deviation): formula for discrete random variables, expectation and variance of linear transformations of random variables, expectation and variance of the average independent and identically distributed random variables. Normal distributions: parameters and properties, the standard normal distribution, the normal probability table, normal quantile plots. E(a+bx) = a + be(x) where a and b are any numbers. Note: a can be positive or negative. E(a + x) = a + ex. Changing x by adding a number to it or by multiplying x by a factor changes the mean. Var(a + b(x) = 2(cid:4666)(cid:1850)(cid:4667)where a and b are any numbers. Variability changes when we rescale, not when we translate. (cid:4666)(cid:1850) (cid:1851)(cid:4667)=(cid:4666)(cid:1850)(cid:4667)+(cid:4666)(cid:1851)(cid:4667), if x and y are independent. Continuous random variables and probability density function. Continuous random variables: can take on any value (real umner) in an interval.