- 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.
approx. 9 hrs
5 topics
21 concepts
Become proficient in working with Continuous Random Variables and achieve success in your examinations.
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.
This learning program is made up of the following 5 topics, broken down into 21 concepts.
Apply the fundamental properties of a probability density function with an unbounded domain
Conditional probability with continuous random variables
Apply the fundamental properties of a probability density function with a bounded domain
Find the percentile, p of a continuous probability distribution
Find the median of a continuous probability distribution
Find the mean or expected value of a continuous probability function, including special results for linear functions
Find the mean or expected value of a continuous random variable X with a probability density function f
Determine the interquartile range of a continuous random variable X with a probability density function f
Find the standard deviation of a continuous random variable X with a probability density function f
Interpret the standard deviation of a continuous probability distribution
Linear transformations and their impacts on the mean and standard deviation of a probability density distribution
Find the variance of a continuous random variable, including special results for linear functions
Use the cumulative distribution function to calculate probabilities
Find the cumulative distribution function given a probability density function defined over a given domain
Apply the definition of the probability density function for a normal distribution to solve problems
Use the 68-95-99.7% rule to solve problems
Calculate the z-value or standardised value
Use a graphics calculator to solve problems given a normal random variable or a normal distribution
Use the normal approximation to the binomial distribution
Use the standard normal distribution definition to sketch graphs of normal distributions given the mean and standard deviation
Use symmetry properties to solve problems with the normal distribution
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