• Mathematical Methods
• Year 12

# Continuous Random Variables

approx. 9 hrs

5 topics

21 concepts

Become proficient in working with Continuous Random Variables and achieve success in your examinations.

Available in
VIC

### Overview

The Year 12 Continuous Random Variables program addresses outcomes from the Statistics and Probability strand in the Australian curriculum. Students studying Year 12 Continuous Random Variables will extend their knowledge of probability by introducing the concept of the probability distribution for a continuous random variable. They also attain proficient skills to calculate and interpret the expected value, variance and standard deviation for a continuous random variable.

### Topics & Concepts We Cover

This learning program is made up of the following 5 topics, broken down into 21 concepts.

• #### Probability Density Function 3 concepts

1. Apply the fundamental properties of a probability density function with an unbounded domain

2. Conditional probability with continuous random variables

3. Apply the fundamental properties of a probability density function with a bounded domain

• #### Mean and Median of Continuous Probabililty Distribution 4 concepts

1. Find the percentile, p of a continuous probability distribution

2. Find the median of a continuous probability distribution

3. Find the mean or expected value of a continuous probability function, including special results for linear functions

4. Find the mean or expected value of a continuous random variable X with a probability density function f

• #### Measures of Spread of Continuous Probabililty Distribution 5 concepts

1. Determine the interquartile range of a continuous random variable X with a probability density function f

2. Find the standard deviation of a continuous random variable X with a probability density function f

3. Interpret the standard deviation of a continuous probability distribution

4. Linear transformations and their impacts on the mean and standard deviation of a probability density distribution

5. Find the variance of a continuous random variable, including special results for linear functions

• #### Cumulative Distribution Function 2 concepts

1. Use the cumulative distribution function to calculate probabilities

2. Find the cumulative distribution function given a probability density function defined over a given domain

• #### Normal Distribution 7 concepts

1. Apply the definition of the probability density function for a normal distribution to solve problems

2. Use the 68-95-99.7% rule to solve problems

3. Calculate the z-value or standardised value

4. Use a graphics calculator to solve problems given a normal random variable or a normal distribution

5. Use the normal approximation to the binomial distribution

6. Use the standard normal distribution definition to sketch graphs of normal distributions given the mean and standard deviation

7. Use symmetry properties to solve problems with the normal distribution

### What you'll get

Learning Content

• A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
• All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

• We match you to a private, expert tutor who is right for your needs and goals
• Our tutors are talented, tested, top ATAR achievers and subject experts
• During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Continuous Random Variables

Reporting

• Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
• You and your parents receive a comprehensive feedback report after every session
• Every session is recorded and available for you to watch at any time, allowing you to review what was covered

### Ready to start this program?

Simply pick a time that works for you

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

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