Titlebook: Probability with Statistical Applications; Rinaldo B. Schinazi Textbook 2022Latest edition Springer Nature Switzerland AG 2022 Probability

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Continuous Random Variables,A . random variable takes all values in a given interval of real numbers.

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The Sample Average and Variance,Let . ≥ 1 be a natural number. Let .., .., ….. be the independent identically distributed (i.i.d. in short) random variables. That is, these . random variables have the same distribution and are independent.

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Estimating and Testing Proportions,We will illustrate the hypothesis testing method on an example.

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Small Samples,In the previous two chapters we have used the Central Limit Theorem to get confidence intervals and perform hypothesis testing. Usually the CLT may be safely applied for random samples of size 25 or larger. In this chapter, we will see alternatives for smaller sample sizes.

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Continuous Joint Distributions,To compute a probability involving two random variables .. and .. we need the joint distribution of (.., ..). In this chapter we will consider only continuous random variables. The joint distribution will be given by the joint density of the random variables.

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Covariance and Independence,The covariance is a measure of dependence between two random variables. Next we give the definition.