ECO2121: Methods of Economic Statistics Additional Examples on Distributions (joint, marginal, conditional) I type this for two reasons: (1) as an example of distributions, and (2) as an example of integration. I hope this can help as some of you are not
ECO2121: Methods of Economic Statistics TA14 15 April 2009 ( 10:23) 1. Simple Linear Regression Remember, regression is just conditional expectation.
=+ + = 1, , We want to know, conditional on X, what is E[Y|X]. X is nonrandom after conditioning, but Y i
ECO2121: Methods of Economic Statistics TA13a 8 April 2009 This is a supplement to TA13. 1. Covariance Cov[X, Y] = E[(X X)(Y Y)] = E[XY] X Y In our example, X = 0.4 and Y = 5, so E[XY] = 13fX,Y(1,3) + 15fX,Y(1,5) + 17fX,Y(1,7) + 02fX,Y(0,2) + 03fX,Y(0,3)
ECO2121: Methods of Economic Statistics TA13 8 April 2009 There is a supplement TA13a. 1. Hypothesis Testing (Two populations) (continued) What is F distribution? F stands for Sir Ronald Fisher. Definition: Suppose W ~ 2(kw) and V ~ 2(kv) independently, t
ECO2121: Methods of Economic Statistics TA12 8 April 2009 1. Hypothesis Testing (Two populations) (continued) Referring to TA10, test at = 0.05 that H0: pX pY = 0, or X Y = 0.
Example 2: Given the following: nX = 51, = 67, sX = 15, and nY = 75, = 78, sY =
ECO2121: Methods of Economic Statistics TA11 1 April 2009 1. Confidence Interval (Two Populations) (continued) Motivation: previously we can construct a C.I. for two independent samples, how about two dependent samples? Example: According to the budget pl
ECO2121: Methods of Economic Statistics TA10 1 April 2009 1. Hypothesis Testing (continued) Example: Given n = 324, x = 233, so = 0.72.
2. Confidence Interval (Two Populations) Motivation: for X ~ Bernoulli(pX), pX is the only parameter, we can find both
ECO2121: Methods of Economic Statistics TA9a 18 March 2009 Excel Functions for Distributions 1. Normal Distribution N(, 2) We know z0.05/2 = 1.96, now we want to know the two following: (a) if we fix an , what is the corresponding z; and (b) if we fix a z
ECO2121: Methods of Economic Statistics TA 8 11 March 2009 1. Parametric Distributions (revisited) Throughout the semester, we deal with parametric distributions, for instance, for Normal distribution N(, 2), and 2 are the parameters; while for Bernoulli
ECO2121: Methods of Economic Statistics TA7 4 March 2009 Writing down explanations for True/False or Multiple Choice questions is stupid. 1. The Budget 0910 (a) Subsidize university fresh graduates: help them to secure a job. (b) Increase tax rate on ciga
ECO2121: Methods of Economic Statistics TA6 25 February 2009 A statistician is like an ice-cream chef. 1. Normal Distribution (a) Suppose X ~ Normal(, 2), then aX+b ~ Normal(a+b, a22). Hence, we get the standardization: Z = (X )/ ~ Normal(0, 1) (b) Suppos
ECO2121: Methods of Economic Statistics TA5 18 February 2009 We continue from TA4 the Exponential distribution. 1. Statistical Inference Two essential elements: Estimation and Hypothesis Testing. 2. Parametric Distribution Some types of distribution are c
ECO2121: Methods of Economic Statistics TA4 11 February 2009 1. What probability distributions/random variables model? Discrete: Hypergeometric, Binomial, Poisson, Bernoulli, Geometric Continuous: Uniform, Exponential, Normal 2. Some important results (a)
ECO2121: Methods of Economic Statistics TA3 4 February 2009 1. Conditional Probability Recall Prcfw_AB = Prcfw_A + Prcfw_B Prcfw_AB Prcfw_ AB = 0 if A and B are mutually exclusive. Suppose not, Prcfw_ AB can be calculated first by conditioning on either e
ECO2121: Methods of Economic Statistics TA2 21 Jan 2009 1. 2. (a) (b) 3. Sample Space S, Event, Probability Measure P and Random Variable X Interpretations of P Subjective Probability Experimental Probability Rules of P Prcfw_ AB = Prcfw_A + Prcfw_B Prcfw
ECO2121: Methods of Economic Statistics TA1 14 Jan 2009 1. Sample Statistics [Exercise 4] Sample Mean x =
x
i =1
n
i
n
2
n xi n n n 2 2 2 2 ( xi x ) xi nx xi i=1 n Sample Variance s 2 = i =1 = i =1 = i =1 n 1 n 1 n 1
2. z-score [Exercise 3] It measures th
ECO2121: Methods of Economic Statistics Summary from TA8 to TA14 For any random variable X, we are interested in its distribution. If it is parameterized, we thus want to estimate the parameters. To construct C.I.s or conduct Hypothesis Testing, the key i
ECO2121: Methods of Economic Statistics TA14a 15 April 2009 This is a supplement to TA14. 1. Example of OLS Estimates Calculations Consider a data set of (Xi, Yi) for i = 1, 2,5, where Xi = years of schooling, Yi = weekly income ($), as follows: Xi (years