Math/Stat 394‚ Winter 2011 F.W. Scholz Central Limit Theorems and Proofs The following gives a self-contained treatment of the central limit theorem (CLT). It is based on Lindeberg’s (1922) method. To state the CLT which we shall prove‚ we introduce the following notation. We assume that Xn1 ‚ . . . ‚ Xnn are independent random variables with means 0 and 2 2 respective variances σn1 ‚ . . . ‚ σnn with 2 2 2 σn1 + . . . + σnn = τn > 0 for all n. 2 Denote the sum Xn1 + . . . + Xnn by Sn and observe
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An Analysis of Transformational Leadership BSP045 Work Psychology B010898 Cheng Chen Introduction Since the early 1980s‚ there has been an explosion of interest on transformational leadership among scholars and managers. It is shown with evidence that the desire and effectiveness of transformational leadership style are universal (Den Hartog‚ et al.‚ 1999‚ and Bass‚ et al. 2006). This leadership style‚ as its name implies‚ is a process which tends to change and transform individuals (Northouse
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As we know that women are always related with sexuality‚ many people use this theme as a main topic of their novels‚ articles or any other literatures; included Wei Hui – one of the controversial Chinese feminist writer – who put women and sexuality as her main topic in her forbidden novel‚ the Shanghai Baby. Having lived in a state of quasi-servitude for over two thousand years‚ Chinese women began to demand liberation from their serfdom within the family clan complex. They sought to outlaw arranged
Free Sexual intercourse Marriage Human sexuality
(a) In general‚ let X1 ‚ X2 ‚ . . . ‚ Xn be a random sample drawn from this distribution. Since 2 1 2 1 7 µ1 = E[X] = 0 · θ + 1 · θ + 2 · (1 − θ) + 3 · (1 − θ) = − 2θ. 3 3 3 3 3 we have θ= and the MME for θ is 7 1 − µ1 ‚ 6 2 7 1 θˆ = − X‚ 6 2 1∑ Xi . In this case‚ we have X = 3/2 and n i=1 n where X = 7 1 3 5 θˆ = − · = . 6 2 2 12 (b) The likelihood function of the sample (3‚ 0‚ 2‚ 1‚ 3‚ 2‚ 1‚ 0‚ 2‚ 1) is lik(θ) = f (3‚ 0‚ 2‚ 1‚ 3‚ 2‚ 1‚ 0‚ 2‚ 1|θ) ( )2 ( )3 ( )3 ( )2 2 1 2 1 = θ · θ · (1 −
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Jim Rice sat in the back seat of a black Mercedes S-class as it drove the streets of Handan. He referred to the city‚ roughly 450 KM south of Beijing‚ as “a small Chinese town of 8.9 million people”. While it wasn’t part of his immediate plans‚ Rice was here to form the ties necessary to set up a future poultry operation. Beside him sat the Vice Mayor for agriculture‚ his chaperone on a tour of the city designed to showcase the quality of its land and its animal husbandry practices. Looking ahead
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Assumptions Consider the univariate linear regression framework: Yi = β0 + β1 Xi + ui Until now‚ it was assumed that E (ui |Xi ) = 0‚ i.e. conditional mean independence. Let’s relax this assumption and allow the covariance between Xi and ui to be dierent from zero. Our problem here is that ui is not observed. Doing OLS yields inconsistent estimates (remember the OVB formula). In this case we refer to Xi as an endogenous variable. The way to get consistent estimates is to use an
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1‚ 2‚ . . . ‚ n and (xi ‚ yi ) : i = 1‚ 2‚ · · · ‚ n are sets of n pairs of numbers‚ then: n n n (ai xi + bi yi ) = i=1 i=1 ai x i + i=1 bi yi 2. FALSE If xi : i = 1‚ 2‚ . . . ‚ n is a set of n numbers‚ then: n n n n n (xi − x) = ¯ i=1 n i=1 2 x2 i − 2¯ x i=1 xi + i=1 x = ¯ i=1 2 x2 − n¯2 x i where x = ¯ 1 n i=1 xi 3. TRUE If xi : i = 1‚ 2‚ . . . ‚ n is a set of n numbers and a is a constant‚ then: n n a xi = a i=1 n i=1 xi = a n x ¯ where x = ¯ 1 n i=1 xi 4. FALSE If X and Y
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Histogram of b0 Figure 2: Histogram of b1 2 i b. As we have known‚ b1 = i i(Xi −X)2 = i (Xii −X)2i = i Ki Yi whereKi = Xi −X¯ 2 ¯ ¯ i i i (Xi −X) So‚ b1 is a linear combination of Yi . Since Yi has a normal distribution‚ b1 also follows a normal distribution. E(b1 ) = i Ki E(Yi ) = i Ki (β0 + β1 Xi ) = i Ki β0 + ( i Ki Xi )β1 ¯ i (Xi −X) =0 ¯ i Ki = (Xi −X)2 i i i i i i i =1 ¯ 2 = ¯ 2 i Ki X i = i (Xi −X) i (Xi −X) E(b1 ) = 0 + 1 ∗ β1
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respected while being a fox is being sly and secretive. Two “New Monarchs” Louis XI of France and Isabella and Ferdinand of Spain used Machiavelli’s advice. While both Monarchs took Machiavelli’s advice to gain wealth through taxation or new industries and power through war‚ Isabella and Ferdinand of Spain took Machiavelli’s advice to heart and took control of Spain with the illusion of being a Christian to be respected‚ Louis XI was indecisive did not capitalize on isolation and relied on luck. That means
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management systems‚ The problem will produce processing for communication‚ resulting in adverse consequences. They could have some disagreement between each other in Susan’s proposal for Wegmans Food Markets. Ming-Shu Hsu Jing Yang Wei Tianhao Zhu LinYan
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