Submission is due at 1pm on Tuesday in Week 3.
Cdf, pdf and moments
A random variable, , has an expectation of and a variance of .
Show that its skewness can be written as
Hence derive an expression for in terms of and for a random variable whose pdf or pmf is symmetric about .
[marks: 5]
The lifetime, , in days of a species of butterfly has a density of
(You discovered the value of in CW01.)
Find the expectation of for . What constraints are there on for the expectation to be finite?
Write down the expectation and variance of .
Using the formula in Skew2, find the skewness of .
[marks: 6]
Una and Ed have just phoned for a taxi. Una suggests modelling their waiting time as but Ed believes is better. Discuss the pros and cons of these options. Note: this question is not asking you to discuss how you would choose or .
[marks: 4]
For a sufficiently smooth function, , Taylor expansion about some point, , gives
for some between and . Consider any function with for all and show that . Hence relate to and to .
[marks: 5]