Log in
Statistics
1
answer
0
watching
9
views

2. The profits of a City Center in Thousand R.O per day has the following probability distribution: 12 14 17 % 24% Profits in Thousand R.O 10 18 % 13% (2 Marks) 19 Marks) Probability (14 Marks) a. Find the value of a. b. Find E(3x+4). C. Find V(5x+2). Page 1 of 4

Watch
1
answer
0
watching
9
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Unlock all answers

Get 1 free homework help answer.
Get unlimited access
Already have an account? Log in
Share

Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions


2. (12 marks) In a study of 85 individuals, food questionnaires were used to measure the change in polyunsaturated fatty acids (PUFA) intake from the beginning to the end of the study. In addition researchers measured a genetic marker in the TNF-αgene; for this analysis, we will take the two values of this TNF-αvariable to be A- or A+. The researchers also collected information on gender, age and BMI. The primary question of interest is whether TNF-αmodifies the effect of PUFA on HDL.
 
(a) (1 mark) Let TNFa be a variable with value 1 for A+ and 0 for A- TNF-αstatus and
let gender be 1 for males and 0 for females. State a linear model for mean change in HDL that includes the predictors PUFA, TNFa, PUFA×TNFa interaction, and effects for gender, age and BMI.
(b) (1 mark) A summary of the fitted model is:
                     Estimate       Std. Error   t value     Pr(>|t|)
(Intercept)     0.037531      0.196980   0.191     0.8494
pufa              0.019143      0.009245    2.071      0.0417
TNFa              0.074433      0.034128   2.181      0.0322
gender          -0.008988      0.031793   -0.283     0.7781
age               -0.003895      0.002156   -1.806     0.0747
bmi                0.006777      0.004332    1.565      0.1217
pufa:TNFa      -0.024575      0.017844  -1.377      0.1724
Write a short sentence to describe why we would even consider removing gender from the model (i.e., why we would not just be happy with the above model from
the outset).
 
(c) (2 marks) Below is a summary of the model fit without gender. Using our 10% rule-of-thumb, is there any evidence that gender confounds the PUFA×TNFa effect?
If so why, if not why not?
                        Estimate     Std. Error      t value       Pr(>|t|)
(Intercept)       0.024467     0.190364      0.129         0.8981
pufa                0.018841     0.009130      2.064         0.0423
TNFa               0.074850     0.033897      2.208         0.0301
age                -0.003783     0.002107    -1.795         0.0765
bmi                 0.006835     0.004301     1.589          0.1161
pufa:TNFa       -0.024496     0.017737   -1.381          0.1712
 
(d) (2 marks) The researchers decided to use the model with PUFA, TNFa, PUFA×TNFa, age and BMI for inference of PUFA×TNFa interaction. What are the degrees of
freedom for the t-distribution whose critical value we need to construct confidence intervals for the interaction? What upper tail probability should you use for a 95%
confidence interval?
(e) (1 mark) The appropriate critical value is 1.96. Construct a 95% confidence interval for the interaction.
(f) (2 marks) State the null hypothesis and a two-sided alternative hypothesis for testing whether TNFa modifies the effect of PUFA on HDL.
(g) (1 mark) From the computer output, what is the p-value for this test?
(h) (2 marks) For fixed age and BMI, what is the estimated effect of a one-unit change in PUFA for a subject who is A- at TNF-α? For fixed age and BMI, what is the estimated effect of a one-unit change in PUFA for a subject who is A+ at TNF-α.

Happy Clown Carnival Company is scheduled to appear in a city on a particular Saturday. The profits that will be obtained depend heavily upon the weather. If the weather is rainy, the carnival loses $15,000; if it is not rainy, the carnival makes a profit of $5,000. Historically, the probability of rain on any given day is 10%.

The carnival has to set up equipment for its show, but it can cancel the show prior to setting up its equipment. Cancelling the show results in a loss of $1,000, regardless of the weather. However, for an additional $250 cost, the carnival can postpone its setup decision until the Friday before the scheduled performance. At that time, the carnival can obtain the local weather forecast for Saturday’s weather.

The Weather Bureau has compiled data on its past forecasts. When it was rainy, the Weather Bureau had predicted rain 74% of the time. When it was not rainy, the Weather Bureau had predicted no rain 86% of the time.

(a) Set up the decision tree and determine the decision (SETUP or CANCEL) that maximizes the expected profit without waiting for a weather forecast on the blank page provided. Leave enough space to add to this tree in part (d).(15 pts for correct tree, 12 pts for decision and backup calculations.)

(b) Determine the Expected Value of Perfect Information (EVPI) for the situation depicted in your decision tree from (a).(7 pts.)

(c) Append to your decision tree in (a) a decision tree diagram that includes waiting for the results of the weather forecast. Be sure to clearly label the branches and nodes. (15 pts.)

(d) Determine the two posterior probability distributions for Saturday’s actual weather given the weather forecasts on Friday and put your results in the appropriate places on your tree in (c). (Hint: Bayes. ). (15 pts.)

(e) . Calculate the Expected Values at each appropriate node for the part of the tree diagram you added in (c). (30 pts.)

(f) Based on your results in (e), what is your optimal decision strategy? (5 pts.)

(g) Calculate the Expected Value of Sample Information (EVSI) and the efficiency of sample information for this situation. Also calculate the Expected Net Gain of Sample Information. (ENGSI is the amount you expect to gain from the sample information after accounting for what it cost you to get that information.) (5 pts.) Use this page for your decision tree. Please write clearly enough so I can tell what your answers are.

consider the following time series data

Week 1 2 3 4 5 6
Value 18 13 16 11 17 14
a. Construct a time series plot. What type of pattern exists in the data?
b. develop a three-week moving average for this time series. Compute mSe and a forecast for week 7.
c. use a 5 0.2 to compute the exponential smoothing values for the time series. Compute mSe and a forecast for week 7.
d. Compare the three-week moving average forecast with the exponential smoothing
forecast using a 5 0.2. Which appears to provide the better forecast based on mSe?
explain.
e. use trial and error to find a value of the exponential smoothing coefficient a that
results in a smaller mSe than what you calculated for a 5 0.2.

Weekly leaderboard

Home
Homework Help 3,900,000
Statistics 10,000
Start filling in the gaps now
Log in