1) Sandra has three suitors and has to decide which to take to the big dance. Their romance, geekiness, and the chance Sandra will choose them are listed below:
|
Suitor
|
Kris
|
Colin
|
Seth
|
|
Romance
|
10
|
7
|
7
|
|
Geekiness
|
6
|
9
|
6
|
|
Choose
|
50%
|
30%
|
20%
|
a) Calculate marginal pdf's of romance and geekiness.
b) Calculate expected romance and geekiness of Sandra's date.
c) Calculate covariance between romance and geekiness. Interpret this value.
d) Calculate the conditional pdf's of romance if geekiness is 6.
e) Calculate expected value and variance of romance if geekiness is 6.
f) Are romance and geekiness statistically independent?
2) Find the critical values for a 1 tail test (5% in the tail) where:
a) df=90 on a t distribution
b) df=17 on a Chi-Squared distribution
c) df1=8, df2=30 on an F distribution
3) Every winter in Canada, an average of 135 people suffer from Chionophobia. Assuming a normal distribution and a standard deviation of 10, calculate:
a) The percentage of cites wherein between 110 and 125 people suffer from Chionophobia.
b) The minimum number of cases of Chionophobia in the top 20% most affected areas.
4) Wayne is trying to maximize his exam studying effectiveness (E) through consuming caffeine (C) and getting a good night sleep (S), as shown through the formula:
E = c2 -s2 -c3 - 4cs
a) Maximize Wayne's studying effectiveness.
b) If S=10-C, maximize Wayne's studying effectiveness using:
i) Internalizing the constraint
ii) The Lagrangean
c) If S=10-C, calculate the direct and indirect effect of an additional unit of caffeine's effect on exam studying effectiveness.
5) People often debate how important Christmas decorations are for the holiday season. Data was collected below on hours of decorating (D) and Christmas enjoyment (C).
a) Calculate the correlation between decorating and Christmas enjoyment. What does this indicate?
b) Use the data below to estimate the following relationship. Briefly summarize decorating's effect on Christmas as seen through the formula:
ct = β1 + β2Dt + εt
|
Observation
|
1
|
2
|
3
|
4
|
|
Decorating
|
5
|
10
|
15
|
30
|
|
Christmas Enjoyment
|
7
|
7
|
8
|
6
|