A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is f(x) kx2 0 x 2 0 otherwise a. Find the value of k and draw the corresponding density curve. [Hint: Total area under the graph of f(x) is 1.] b. What is the probability that the lecture ends within 1 min of the end of the hour? c. What is the probability that the lecture continues beyond the hour for between 60 and 90 sec? d. What is the probability that the lecture continues for at least 90 sec beyond the end of the hour?

STAT 2004 Week 2 Lecture 4 Wed. 01/25/17 Causation: one variable causes or creates the change in another variable Simple random sample: all observations in the sample have equal chance of being selected Survey question: what is your weight (asking football team) Create a sample frame: list of all potential respondents (list of all 116 players) ID Weight -randomly select 5 values (n=5) 1 118 76,114,90,91,108 2 230 -obtain data from those 5 values 3 211 116 200 X76283 X 114284 X =290 X =30891 108283 Population Parameter of interest: mean weight ( weight) Estimate: sample statistic 283+284+308+293+283 ^=