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Math 150.1 UPD

The Math 150.1 course at the University of the Philippines Diliman covers Mathematical Statistics I, focusing on combinatorial probability, probability distributions, random variables, and sampling distributions. It includes topics such as conditional probability, discrete and continuous distributions, and the Central Limit Theorem. Prerequisites include Math 23 and Stat 101, with a total of 3 credit units and 3 hours of instruction per week.

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Jeremy Neile Cruz
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68 views2 pages

Math 150.1 UPD

The Math 150.1 course at the University of the Philippines Diliman covers Mathematical Statistics I, focusing on combinatorial probability, probability distributions, random variables, and sampling distributions. It includes topics such as conditional probability, discrete and continuous distributions, and the Central Limit Theorem. Prerequisites include Math 23 and Stat 101, with a total of 3 credit units and 3 hours of instruction per week.

Uploaded by

Jeremy Neile Cruz
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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INSTITUTE OF MATHEMATICS

College of Science
University of the Philippines Diliman

Math 150.1 Course Syllabus

A. Course Catalogue Description


Course Number Math 150.1
Course Title Mathematical Statistics I
Course Description Combinatorial probability; probability distributions; joint and conditional
distributions; random variables; distributions of functions of random vari-
ables; mathematical expectation; moment-generating functions; sampling
distributions
Prerequisite Math 23/equiv. and Stat 101/equiv.
Course Credit 3 units
Number of Hours 3 hours/week
B. Course Content
I. Course Introduction and Orientation
II. Probability Space
1. Outcome space, sigma field and probability measure
2. Conditional probability and its properties
3. Independent Events and Bayes’ Rule
III. Random Variables and Distribution Functions
1. Random variables (continuous and discrete)
2. Distribution Functions
a. Cumulative distribution function
b. Probability density/mass functions
c. Moment generating functions
3. Mathematical Expectation
4. Raw and central moments, mean and variance
5. Chebyshev’s Inequality
IV. Discrete Distributions
1. Uniform (Empirical) distribution
2. Bernoulli and Binomial distributions
3. Hypergeometric distribution
4. Poisson distribution
5. Geometric and Negative Binomial distributions
V. Continuous Distributions
1. Uniform (Rectangular) distribution
2. Normal distribution
3. Exponential distribution
4. Other distributions
a. Gamma distribution
b. Beta distribution
c. Lognormal distribution
VI. Multivariate Distributions
1. Joint distributions
2. Marginal distributions
3. Marginal expectations
4. Covariance and correlation
5. Conditional expectations
6. Bivariate Normal distribution
VII. Sampling Distribution
1. Sampling, sample mean and sample variance
2. Law of Large Numbers
3. Central Limit Theorem

For a more detailed syllabus, send an email request to ddapr@math.upd.edu.ph.

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