Description:
Basic statistical concepts and principles, probability distributions of random variables and their uses, linear functions of random variables, and their applications to data analysis and inference. Estimation techniques for unknown parameters, hypotheses testing, and non-parametric tests.
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Topics:
1. Basic Concepts of Probability and Statistics
a. Definition of Statistical Concepts and Principles
b. Uses and Importance of Statistics and Statistical Analysis
c. Central Tendency and Variability of Data
d. Basic Concepts of Probability
2. Discrete Probability Distributions
a. Random Variables and their Probability Distributions
b. Cumulative Distribution Functions
c. Expected Values of Random Variables
d.The Binomial Distribution
e. The Poisson Distribution
3. Continuous Probability Distribution
a. Continuous Random Variables and their Probability Distributions
b. Expected Values of Continuous Random Variables
c. Normal Distribution
d. Normal Approximation to the Binomial and Poisson Distributions
e. Exponential Distribution
4. Joint Probability Distribution
a. Two or More Random Variables
i. Joint Probability Distribution
ii. Marginal Probability Distribution
iii. Conditional Probability Distribution
iv. More than Two Random Variables
b. Linear Functions of Random Variables
c. General Functions of Random Variables
5. Sampling Distribution and Point Estimation of Parameters
a. Sampling Distribution and the Central Limit Theorem
b. General Concept of Point Estimation
i. Unbiased Estimator
ii. Variance of a Point Estimator
iii. Standard Error
iv. Mean-Squared Error of an Estimator
6. Statistical Intervals
a. Confidence Intervals: Single and Multiple Samples
b. Prediction Intervals
c. Tolerance Intervals
7. Inferential Statistics
a. Tests of Hypotheses for a Single Sample
i. One-sided and Two-sided Hypotheses
ii. P-value in Hypothesis Tests
iii. General Procedure for Test of Hypothesis
iv. Test Concerning Means, Variation, and Proportion
b. Statistical Inference for Two Samples
i. Tests Concerning Means, Variance, and Proportions
c. Non-Parametric Tests
i. Runs Test of Randomness
ii. Tests for the Mean: Sign Test, Rank Sum Test, Signed Rank Sum Test
iii. Kruskal-Wallis Test
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