Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. The article Blade Fatigue Life Assessment with Application to VAWTS (J. Solar Energy Engr., 1982: 107111) proposes the Rayleigh distribution, with pdf f(x; ) x 2 e x2 /(2 2 ) x 0 0 otherwise as a model for the X distribution. a. Verify that f(x; ) is a legitimate pdf. b. Suppose 100 (a value suggested by a graph in the article). What is the probability that X is at most 200? Less than 200? At least 200? c. What is the probability that X is between 100 and 200 (again assuming 100)? d. Give an expression for P(X x).

STAT 2004 Week 2 Lecture 5 Fri. 01/27/17 Observational study: data analysis where researcher does not interfere with data outcomes Experiment: researcher directly interferes with data outcomes y imposing treatments and controls Observational An example of an observational study would be a survey: did you get a flu shot Observational studies help establish correlation Experiment Randomly assign a treatment group (flu shot) and a control group (no flu shot) Help establish causation Sample frame: data has to be assigned with a number (a list of people, each have a number that doesn’t repeat) 194,147,134,33,62 Strata: (singular- stratum): subgroups or demographics of a population Stratified random sample: first break population into stra