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Topic_5.0___Probability_Distributions

# Topic_5.0___Probability_Distributions - Probability...

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Probability Distributions Ash Genaidy

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Topic Outline Probability distributions – likelihoods for possible outcomes of a variable. Normal distributions – bell-shaped curve that is the most important probability distribution for statistical analysis. Sampling distributions – distributions for possible values of a sample statistic such as the sample mean. Importance of normal distributions – a bell- shaped curve approximates most distributions used in statistical inferences.
Connection Between Probability and Statistical Inference Inferential statistical methods use sample data to make predictions about the values of useful summary descriptions (i.e., parameters) of the population of interest. In this discussion, we treat parameters as known numbers. This is artificial since parameter values are unknown or we would not need inferential methods.

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Connection Between Probability and Statistical Inference However, many inferential statistical methods involve comparing observed sample statistics to the values expected if the parameter values equaled particular numbers. If the data are inconsistent with particular values, then we infer that actual parameter values are somewhat different.
Using a relative frequency approach, the probability of an outcome is the proportion of times that the outcome would occur in the long run in repeated observations. A probability distribution for a variable lists the possible values of the variable together with their probabilities. Let y denote a possible outcome for the variable Y and let P(y) denote the probability of that outcome. Then, 0 <= P(y) <= 1 and

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Topic_5.0___Probability_Distributions - Probability...

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