review midterm econ 346

review midterm econ 346 - Random Variable : a variable...

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Random Variable : a variable whose value is determined by the outcome of an experiment. Probability A probability distribution function (PDF) P[Xi] for a discrete random variable X assigns probabilities to the possible values X1, X2…Xn. It shows how the probabilities are spread over or distributed over the various values of random variable. For a continuous random variable, it measures the probability of a certain range or interval. The expected (mean) value of a discrete random variable X: A cumulative distribution function (CDF) is the sum of the PDF values of X less or equal to a given x. The normal distribution is completely characterized by its mean (μ) and variance (s 2). Meaning if you know that the population is normally distributed with the values of mean and variance known to you, then you will be in a position to analyze any relevant statistical properties of this population. When a random variable X is known to be normally distributed, we say, in short, that
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Example 2) The daily sale of bread, X, in a bakery, follows the normal distribution with a mean of 70 loaves and a variance of 9. 1. Distribution The distribution of a data set is a table, graph, or formula that provides the values of the observation and how often they occur (probability). 1.1 Distribution Shapes • With a symmetrical distribution a vertical line can be drawn through the middle so that each side is a mirror image of the other. • With a skewed distribution the scores tend to pile up at one end and tail off at the other. • If the tail is to the right the distribution is said to be positively skewed, if the tail is to the left it is negatively skewed.
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2. SAMPLING Population: The entire group of items that interests us. Defined by the characteristics Sample: The part of population that actually observed. Why sampling To draw inferences about the population since it is often impractical to scrutinize the entire population. It is too expensive to apply to the entire population. Biased Sample : Any sample that differs systematically from the population. It can give the distorted picture of the population and may lead to unwarranted conclusion. 1) Sample Selection Bias : The selection of samples systematically excludes or under-represents certain group. Self-selection bias 2) Survivor Bias : a sample from a current population in order to draw inferences about a past population who are no longer around. 3) Nonresponse Bias: The systematic refusal of some groups to participate in an experiment or to respond to a poll. Random Selection : A representative set of sample points drawn randomly from the population is called a random sample. Give an equal chance of inclusion in the sample. Population and Sample Distributions
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review midterm econ 346 - Random Variable : a variable...

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