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Probability and statistics

Course Description: Introduction to probability, binomial and Poisson distributions. Normal approximation to the binomial distribution. Sampling, some important statistics, sampling distribution, sampling distribution of the mean and the difference between two means for large samples, S2 sampling, t-distribution, F-distribution. Statistical inference, classical estimation method, estimation of the mean, standard error of point estimation, prediction interval, estimation of the difference between two means (for known and unknown (equal) variances), estimation of proportion, determination of sample size for a specified error. Null and alternative hypotheses, Type I error, Type II error, one- and two-tailed tests, P-value, tests related to a single mean, tests on two means (for known and unknown variance), test on a single proportion. Least squares and the fitted model, properties of least squares estimators, inference on regression coefficients, prediction, analysis of variance, correlation, multiple linear regression, estimation of coefficients, properties of least squares estimators, inference in multiple linear regression, nonlinear regression models.

Credit hours: 3

Prerequisites: MATH203

Objectives of the course :

1. Description and identification of the binomial, Poisson, normal, and normal approximation to the binomial distributions.

2. Familiarity with the basic concepts of sampling and sampling distributions.

3. The ability to understand estimation problems using means, prediction intervals, confidence intervals, and proportions.

4. Classification of Statistical Hypothesis Testing Methods for Decision Making.

5. The ability to identify correlation coefficients and estimation coefficients.

6. Description and identification of linear regression, multiple linear regression, and data fitting using the least squares method.

Course outputs :

1. Define the concept of probability using binomial, Poisson, and normal distributions.

2. Define the t-distribution, F-distribution, sampling distributions, and describe data.

3. Describe the principles of estimating the single mean, the difference between means, the proportion, and the prediction interval, with known and unknown variance.

4. Define the null and alternative hypotheses for a single mean, a difference of means, and a proportion, with known and unknown variance.

5. Explain the concepts of linear regression, multiple linear regression, nonlinear regression models, the least squares method, and forecasting.

6. Calculate the probability using binomial, Poisson, and normal distributions.

7. Calculate probability using the t-distribution and F-distribution.

8. Estimate the probability of the sample mean and the difference between means when the variance is known and unknown. 9. Calculate the confidence interval and prediction interval for the population mean, difference of means, proportion, and variance.

10. Solve hypothesis tests for one and two samples, and state the result.
11. Calculate the correlation coefficients and regression coefficients.

12. Discuss multiple linear regression, coefficient estimation, properties of least squares estimators, and inferences in multiple linear regression.

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Last updated: 2026-05-17