qm-4-ux4e1ik5.jpg qm3-kqg5doli.jpg qm2-2qfmp42a.jpg qm-1-pvhi21v3.jpg qm9-rf5txrvc.jpg qm-9-v3xmig22.jpg qm-7-jyncljts.jpg qm-6-vj4lytcn.jpg QME May 24, 2018 Contents Part 1. Probability and...

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This is the test, the time is 12:00 Beijing time on November 17. I need to write by hand. I want to find two experts to write for me. Because of the lack of time, Excel software is needed to do the whole process. The test questions can only be sent to you with pictures


qm-4-ux4e1ik5.jpg qm3-kqg5doli.jpg qm2-2qfmp42a.jpg qm-1-pvhi21v3.jpg qm9-rf5txrvc.jpg qm-9-v3xmig22.jpg qm-7-jyncljts.jpg qm-6-vj4lytcn.jpg QME May 24, 2018 Contents Part 1. Probability and Statistical Inference 1 Chapter 1. Descriptive Statistics 2 1.1. Summary statistics for central tendency and extremes 4 1.2. Percentiles and quartiles 8 1.3. Summary statistics for variation 9 1.4. Histogram 10 1.5. Correlation 16 Chapter 2. Introduction to Probability 21 2.1. Theory 21 2.1.1. Sets and Events 21 2.1.2. Probability definition 23 2.1.3. Probability interpretations 26 2.1.4. Probability calculations 28 2.2. Applications 32 2.2.1. Random Drug Testing 32 2.3. Exercises 37 Chapter 3. Discrete Random Variables 40 3.1. Discrete and Continuous Random Variables 40 3.2. Probability 41 3.3. Expected Value and Variance 43 3.4. Bivariate probability distributions 46 3.5. Expected values, Covariance and Correlation 48 3.6. Some rules with expected values 50 3.7. Conditional probability 54 3.8. Conditional expected values 55 Chapter 4. Continuous Random Variables 60 4.1. Cumulative Distribution Function 60 4.2. Quantile Function 64 4.3. Probability Density Function 66 4.4. Expected values, Variance and Moments 68 4.5. Further Examples 74 v CONTENTS vi 4.5.1. Normal distribution 74 4.5.2. t distribution 75 4.5.3. Pareto distribution 75 Chapter 5. Statistical Inference 76 5.1. Statistical Inference 76 5.2. Random sampling 78 5.3. Estimation and Sampling Distributions 81 5.4. Statistical Properties of Mean Estimation 84 5.4.1. Bias and Variance 84 5.4.2. Large sample properties 86 5.5. Hypothesis Testing 88 5.5.1. Components of a hypothesis test 88 5.5.2. Decision rules for one tailed tests 89 5.5.3. Interpretation of the significance level 92 5.5.4. Critical value decision rules 92 5.5.5. Decision rules for two tailed tests 94 5.5.6. Using the normal distribution for critical values 98 5.5.7. Power 99 5.6. Confidence Intervals 101 Part 2. Linear Regression 104 Chapter 6. Simple Regression 105 6.1. Concepts and Methods 105 6.1.1. From two means to regression 105 6.1.2. Population Regression Function 106 6.1.3. Sample Regression Function 109 6.1.4. Goodness of fit 111 6.1.5. Inference 113 6.1.6. Prediction 118 6.2. Computations 121 6.2.1. Excel: SRF by formulae 121 6.2.2. Excel: Hypothesis test on slope coefficient 122 6.2.3. Excel: SRF using Data Analysis Tool 124 6.2.4. Excel: Slope coefficient inference using Data Analysis Tool 128 6.2.5. Excel: Conditional mean estimation by direct calculations 130 6.2.6. Excel: Conditional mean estimation by transformed regression 130 6.2.7. R: SRF, significance and confidence intervals 133 6.2.8. R: Coefficient testing by transformed regression 134 6.2.9. R: Conditional mean by transformed regression 135 CONTENTS vii 6.3. Applications and interpretations 136 6.3.1. Wages and the city 136 6.3.2. Wages and Education 140 6.3.3. Chocolate and Nobel Prizes 146 6.3.4. Interpretation of regression relationships 148 6.4. Derivations 151 6.4.1. OLS estimators 151 6.4.2. R-squared 156 6.4.3. Regression on an intercept 157 6.4.4. Regression on an intercept and dummy variable 158 6.4.5. Prediction Theory 160 6.4.6. Unbiasedness 164 6.5. Exercises 167 Chapter 7. Multiple Regression 168 7.1. Concepts and Methods 168 7.1.1. Population Regression Function 168 7.1.2. Relationship between short and long regressions 170 7.1.3. Sample Regression Function 172 7.1.4. Goodness of fit 173 7.1.5. Inference 173 7.1.6. Functional forms 173 7.2. Computations 173 7.3. Applications 174 7.4. Derivations 174 Part 3. Further Topics 175 Chapter 8. Statistical Properties and Statistical Inference 176 8.1. Statistical inference and Sampling distributions 176 8.1.1. Simple random sample 176 8.1.2. The Sample Mean 176 8.1.3. Bias 177 8.1.4. Illustration by Simulation 177 8.2. Unbiasedness of OLS 182 8.2.1. Derivation for a simple random sample 182 8.2.2. Illustration by simulation 183 8.2.3. An example of bias with OLS 189 8.3. Asymptotic Concepts 192 8.3.1. Consistency 193 8.3.2. Weak Law of Large Numbers 194 CONTENTS viii 8.3.3. Simulation illustration of the WLLN 194 8.3.4. Asymptotic Distributions 196 8.3.5. Central Limit Theorem 197 8.4. Asymptotic Properties of OLS 200 8.4.1. Consistency of OLS 200 8.4.2. Asymptotic Normality of OLS 201 8.4.3. Simulation illustration 202 8.4.4. Standard Errors 204 8.4.5. Homoskedasticity and OLS standard errors 205 8.4.6. Application: CO2 emissions and economic activity 206 8.5. Asymptotic Properties of 2SLS 208 8.5.1. Consistency of 2SLS 209 8.5.2. Asymptotic Normality of 2SLS 211 8.5.3. Standard errors 212 8.6. Some statistical inference with 2SLS 212 8.6.1. HC t-tests and confidence intervals 213 8.6.2. Joint tests and IV relevance 215 8.6.3. Overidentifying restrictions test 217 Chapter 9. Time Series 220 9.1. Preliminary Concepts 220 9.1.1. Data collected over time 220 9.1.2. On the nature of statistical inference with time series 222 9.1.3. Dependence 223 9.2. Prediction 225 9.2.1. Not causality 225 9.2.2. Conditional expectations and Prediction 225 9.2.3. Forecasting 226 9.2.4. In practice 227 9.2.5. Forecasting further ahead 230 9.3. General Linear Forecasting Models 234 9.3.1. Single equations — AR and ARDL 234 9.3.2. Vector Autoregression 235 9.4. Lag Length Selection 236 9.4.1. Residual autocorrelation 237 9.4.2. Akaike Information Criterion 237 9.5. Application: Inflation and Interest Rates 238 Part 1 Probability and Statistical Inference CHAPTER 1 Descriptive Statistics Descriptive statistics, as the name suggests, involves the use of graphs and/or a small number of summary statistics to describe some interesting features of some data. The contrast with statistical inference, discussed later on, is that descriptive statistics are not intended to be taken as informative about some underlying larger population. Example 1.1. (a) Your academic transcript at the University of Melbourne will include a “WAM”, es- sentially the average of the marks (out of 100) that you receive for each subject you study. This average is a summary statistic, and describes one aspect (the overall level, measured in marks) of your academic achievements. Your WAM is not intended to be an estimate of some other measure, eg the average marks across all students in your year, or the average mark you would get if you took more subjects at the University of Melbourne. The WAM is intended to be simply a descriptive statistic to summarise of your academic performance. (b) However the same average mark could also be used for inference rather than description. Suppose you finish your first degree and want to apply to study in a Masters program next. The Masters program will accept only students with higher WAMs in their first degree, in the belief that higher undergraduate WAM predicts greater chances of success in a Masters program. This would be an example of statistical inference (at least informally) in the sense that the statistics are being used to make inferences/predictions beyond the observed marks, i.e. future marks being predicted on the basis of observed marks. (c) Suppose some researchers set up at the entrance to the lecture theatre at the start of a QM1 lecture and ask 100 randomly selected students how they got to campus that day 2 http://ask.unimelb.edu.au/app/answers/detail/a_id/5745/related/1 1. DESCRIPTIVE STATISTICS 3 — train, tram, bus, bike, car, or walk. They find 21 out of the 100 students took the tram, i.e. 21%. Then, for the purposes of public transport service planning, they use this summary statistic as an estimate of the percentage of all students who take trams to the university each day. This last step, taking the summary statistic of 21% as an estimate of a statistic for a larger unknown population, is statistical inference. (d) In late 2017 and early 2018, Australia and England played a series of five test cricket matches. The scores made by the respective captains through the series were1 Steve Smith (Australia) : 141, 40, 6, 239, 76, 102, 83 Joe Root (England) : 15, 51, 9, 67, 20, 14, 61, 83, 58 giving averages (means) of 98.14 for Steve Smith and 42 for Joe Root. Used as descrip- tive statistics, these averages indicate that Steve Smith had an outstanding series, more than twice as good as Joe Root, whose own series was still quite good. 1If you don’t know about cricket, it is sufficient to know that higher scores are better, and to score 100 or more is very good. If you do know about cricket, to keep things simple “not out” innings are treated as complete innings here. http://www.yarratrams.com.au/using-trams/getting-around/timetables/ https://www.ptv.vic.gov.au/stop/view/51582/ https://www.youtube.com/watch?v=VWGqGHMO294 http://www.espncricinfo.com/australia/content/player/267192.html http://www.espncricinfo.com/england/content/player/303669.html 1.1. SUMMARY STATISTICS FOR CENTRAL TENDENCY AND EXTREMES 4 If we took the additional step of concluding from these averages that Smith is overall more than twice as good as Root as a test cricket batsman, we would be shifting from descriptive to inferential statistics — using a relatively small set of observations to infer some conclusion about the totality of the players’ test careers that would extend over many years and many series. This leap from description to inference in this situation would seem intuitively doubtful. The point of studying statistical inference is to set up some rigorous rules to understand how well such steps from description to inference might work in different situations. � In this chapter we consider only descriptive statistics. Statistical inference is a conceptually more complicated task and is covered later. 1.1. Summary statistics for central tendency and extremes Suppose we have some observations denoted X1, X2, . . . , Xn. For example the scores of Steve Smith in Example 1.1(d) above would be denoted X1 = 141, X2 = 40, X3 = 6, . . . , X7 = 83, with n = 7. Definition 1.1. Mean. The mean of
Answered Same DayNov 12, 2021

Answer To: qm-4-ux4e1ik5.jpg qm3-kqg5doli.jpg qm2-2qfmp42a.jpg qm-1-pvhi21v3.jpg qm9-rf5txrvc.jpg...

Rajeswari answered on Nov 17 2021
136 Votes
Multiple choice qns
Q.no.1
a) E(Y/x=0) = sum of conditional p*Y = 0(0.6)+1(0)+2(0.4) = 0.8
b) E(Y/x=1)=0(0.1)+1(0.2)+2(0.7) = 1.6
c) First we must
get pdf of X
P(x=0) = 0.5 and P(x=1) = 0.5
E(x) = 0.5
d) E(x^2) = 1(0.5) = 0.5
Var(x) = 0.5-0.25 = 0.25
d) Jt prob distribution of x and y
     
    x
    0
    1
    y
     
     
     
    0
     
    0.3
    0.05
    1
     
    0
    0.1
    2
     
    0.2
    0.35
f) Marg pdf of Y is P(Y=0) = 0.35, P(Y=1) = 0.1 and P(Y=2) = 0.55
g) P(X/y=0) is
    condl y =0
     
     
    x
    0
    1
    Prob
    0.6
    0.4
h) conditional EV = E(x/y=0) = 0(0.6)+1(0.4) = 0.4
i) E(X^2/y=0) = 0^2(0.6)+1^2(0.4) = 0.4
Var(X/y) = 0.4-0.16 = 0.24
j) P(X=0, y = 0) = 0.3 and P(x=0) *P(y-0) = 0.5*0.35
Since the two are not equal they are not independent.
Q.no.2
Total children -130
Prefer coke = 75
p = Sample proportion =75/130 =
    p
    0.576923
    q
    0.423077
    SE
    0.043331
    H0
    p=0.5
    Ha
    p<0.5
(one tailed test at 5% level)
Margin of error for 95% = 1.96*sE =
    Mar of error
    0.084928
    CI LB
    0.491995
    UB
    0.661851
1) Test statistic z = p difference/SE = 0.076923/0.043331=1.772
P value = 0.038
Since p value is less than 0.05 we reject H0.
2.) 95% conf interval for proportion of coke prefers = (0.5769,0.6619)
Since 0.50 is not contained in this we reject null hypothesis.
The decision rule is reject H0. Same decision we got in 1.
Qno.3
Given that n = 42, x bar = 4.8, std dev = 0.8 seconds
Another server n = 42, y bar = 4.5 and stddev = 0.6 seconds
Mean difference =...
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