Statistics Assignment Help
Independence. Three events A, B, and C are pairwise independent
if each pair is independent. They are mutually independent if they are pairwise independent
and in addition
P(A ∩ B ∩ C) = P(A)P(B)P(C). (1)
Suppose we roll two 6-sided die. Consider the events:
A = ‘odd on die 1’ B = ‘odd on die 2’ C = ‘odd sum’
Are A, B, and C pairwise independent? Are they mutually independent?
Consider the Venn diagram below. A, B and C are the overlapping circles and the
probabilities of each region are as marked. Does equation (1) hold. Are the events A, B, C
mutually independent?
- 0.225 0.225
- 0.175 . Are the events A, B, C
- mutually independent?
- 0.225 0.225
- 0.175
- 0.05
- 0.1 0.1
- 0.125
- A
- C
- B
For families with n children, the events ‘the family has children of both sexes’ and ‘there
is at most one girl’ are independent. What is n?
Problem 2. (10 pts.) R simulation. Suppose there is an experimental medical treatment
for a cancer that if untreated is nearly always fatal within 12-15 months. The doctors enroll
5000 patients in a study in which each patient is given the treatment and followed for 5
years. Let X be the length of time a random patient given the treatment survives. (If a
patient is still alive at the end of the study, then X = 5 for this patient.)
As the statistician it is your job to analyze the data. To put the data in a vector x you
need to do the following.
First download ps3prob2data.r (you can find it on the 18.05 OCW site) and put the file in
your R working directory. Then give the the following R commands.
> source(‘ps3prob2data.r’)
> x = getprob2data()
Compute the mean and standard deviation of the data.
