# Theory of Probability, Short Course

• 2 months
Duration
Probability spaces as models for phenomena with statistical regularity. Discrete spaces (binomial, hypergeometric, Poisson). This Theory of Probability course is offered by Stanford Summer.

## Overview

International students who require a Stanford-sponsored I-20 visa must maintain a minimum of 8 units throughout the Summer Quarter.

Stanford Summer Session provides high-achieving and ambitious students a transformative educational experience at a world-class university.

By combining challenging academics with a rich array of extra-curricular programming, Stanford Summer Session successfully shares the University’s culture of innovation, academic excellence, and global responsibility.

#### Program highlights

Upon successful completion of the Theory of Probability course offered by Stanford Summer, students should be able to:

• Discuss axioms and basic defnitions of probability
• Define the concepts of independence and conditional probabilities
• Compute probabilities using basic combinatoric techniques
• Identify discrete and continuous random variables and related density functions
• Evaluate mathematical expectation and variance of a random variable
• Interpret limit theorems in probability (e.g., weak/strong law of large numbers, central limit theorem)

## Detailed Programme Facts

• More details:

• Programme intensity Full-time
• Full-time duration 2 months
• Duration description

8 Weeks

• Credits
3-5 alternative credits
• Languages
• English
• Delivery mode
On Campus

## Programme Structure

Course content:

• Axioms of probability
• Basic Combinatorics
• Conditional probability and independence
• Discrete random variables
• Continuous random variables
• Expected value and variance
• Limit theorems
• Markov chains

## English Language Requirements

• Minimum required score:

6.5

The IELTS – or the International English Language Test System – tests your English-language abilities (writing, listening, speaking, and reading) on a scale of 1.00–9.00. The minimum IELTS score requirement refers to which Overall Band Score you received, which is your combined average score. Read more about IELTS.

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• Minimum required score:

100

The TOEFL iBT ® measures your English-language abilities in an academic setting. The test has four sections (reading, listening, speaking, and writing), each with a score range of 0-30, for a total score range of 0-120. Read more about TOEFL iBT ®.

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## General Requirements

International students who require a Stanford-sponsored I-20 visa must maintain a minimum of 8 units throughout the Summer Quarter.

• Original I-20 (Certificate of Eligibility for Nonimmigrant F-1 Student Status)
• I-901 SEVIS Fee Receipt
• Stanford University's Stanford Summer Session Admission Letter (available online within the Stanford Summer Session applicant status page)
• Original Proof of Funding Document
• F-1 Visa (this is the visa stamp attached to your passport by the U.S. Embassy)
• Passport

## Tuition Fee

• ### International Applies to you

1175 USD/credit
Tuition Fee
Based on the original amount of 1175 USD per credit and a duration of 2 months.
We've labeled the tuition fee that applies to you because we think you are from and prefer over other currencies.

Tuition fee does not include:

• Application fee
• Housing and meals
• Healthcare coverage plan

## Living costs for Stanford

• 1100 - 1600 USD/month
Living Costs

The living costs include the total expenses per month, covering accommodation, public transportation, utilities (electricity, internet), books and groceries.

## Funding

Check the programme website for information about funding options.

Studyportals Tip: Students can search online for independent or external scholarships that can help fund their studies. Check the scholarships to see whether you are eligible to apply. Many scholarships are either merit-based or needs-based.

##### Theory of Probability
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