Summary Chapter 1-7 Chapter 1 * Population – consists of members of a group which you want to draw a conclusion * Sample – portion of population * Parameter – numerical measure that describes a characteristic of a population * Statistic – numerical measure that describes a characteristic of a sample * Descriptive statistics – collecting‚ summarizing and presenting data e.g. survey * Inferential statistics – drawing conclusions about a population based on sample data
Premium Normal distribution Probability theory Random variable
of hypothesis for a single mean (σ unknown): t= 1 ¯ −µ X √ S/ n Z-test of hypothesis proportion: for a single Z-test for the difference between two means (variances known): p−π Z∼ = Z= π(1−π) n t-test for the difference between two means (variances unknown): t= 1 n1 + + (¯ x1 − x ¯2 ) ± tn1 +n2 −2 1 n2 Pooled variance estimator: Sp2 = σ12 n1 t= sd x ¯d ± tn−1 √ n ¯ d − µd X √ Sd / n Z= (P1 − P2 ) − (π1 − π2 ) P (1 − P ) R1 + R 2 n1 + n2 (p1 − p2 ) ± z χ2 test of association:
Premium Sample size Variance Arithmetic mean
Use Definition 4.3 on page 120 to find the variance of the random variable X of Exercise 4.7 on page 117. 4.7 By investing in a particular stock‚ a person can make a profit in one year of $4000 with probability 0.3 or take a loss of $1000 with probability 0.7. What is this person’s expected gain? 4.37 A dealer’s profit‚ in units of $5000‚ on a new automobile is a random variable X having the density function given in Exercise 4.12 on page 117. Find the variance of X. 4.12 If a dealer’s profit‚ in units
Premium Random variable Probability theory Variance
Male 382 3.01 2.648 .135 Female 524 3.00 2.497 .109 Independent Samples Test Levene’s Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper Hours per day watching TV Equal variances assumed .221 .638 .068 904 .946 .012 .172 -.327 .350 Equal variances not assumed .067 792.603 .947 .012 .174 -.330 .353 There is no significant difference between male(mean=3.01
Premium Normal distribution Standard deviation Variance
Gaussian Mixture Models∗ Douglas Reynolds MIT Lincoln Laboratory‚ 244 Wood St.‚ Lexington‚ MA 02140‚ USA dar@ll.mit.edu Synonyms GMM; Mixture model; Gaussian mixture density Definition A Gaussian Mixture Model (GMM) is a parametric probability density function represented as a weighted sum of Gaussian component densities. GMMs are commonly used as a parametric model of the probability distribution of continuous measurements or features in a biometric system‚ such as vocal-tract related
Premium Normal distribution Variance
1 . (a) What do you understand by the concept of conservatism ? Why is it also called the concept of prudence? Why is it not applied as strongly today as it used to be in the Past ? (b) What is a Balance Sheet ? How does a Funds Flow Statement differ from a Balance Sheet ? Enumerate the items which are usually shown in a Balance Sheet and a Funds Flow Statement. 2 . (a) Discuss the importance of ratio analysis for inter-firm and intra-firm comparisons including circumstances responsible
Premium Standardization Economics Financial statements
ECM1000 Research Methods in Finance Lecture 9 Autocorrelation 1 Outline • • • • Introduction Consequences of Autocorrelated Disturbances Detecting Autocorrelation Remedy References: Gujrati‚ Ch. 12 Introduction Imagine that we are fitting the regression equation to a set of economic variables observed through time: yt xt1 ........ xtk ut Then it is usual to assume that the disturbance ut represents the net effect of everything not accounted for by the systematic part of
Premium Regression analysis Variance Linear regression
The 10 stocks are being selected for portfolio 1 among the 15 stocks due to having the highest market capitalization. It is a measurement derive from share price times the number of shares outstanding. In addition‚ it could be represent the public opinion of a company’s net worth. Undoubtedly‚ these 10 stocks are chosen because of having the highest company’s value‚ highest expectation from the public and both highest economic and monetary conditions. Although sometime market cap might be an economic
Premium Investment Variance Standard deviation
Practice Multiple Choice Questions for Exam 2 Prof. Alex Angelus Sept. 20‚ 2014 Question 1 2. Which of the following regarding the mean and variance of a portfolio of two stocks is false? a. . b. . \ c. d. . 2 Question 2 2. Which of the following are required conditions for the distribution of a discrete random variable X that can assume values xi? a. 0 p(xi) 1 for all xi b. c. Both a) and b) are required conditions d. Neither a) nor b) are required conditions
Premium Normal distribution Standard deviation Variance
Think Stats: Probability and Statistics for Programmers Version 1.6.0 Think Stats Probability and Statistics for Programmers Version 1.6.0 Allen B. Downey Green Tea Press Needham‚ Massachusetts Copyright © 2011 Allen B. Downey. Green Tea Press 9 Washburn Ave Needham MA 02492 Permission is granted to copy‚ distribute‚ and/or modify this document under the terms of the Creative Commons Attribution-NonCommercial 3.0 Unported License‚ which is available at http://creativecommons
Premium Normal distribution Variance