analyse a probability mass function or probability density function and the shape of its graph in terms of the defining parameters for the probability distribution and the mean and variance of the probability distribution
U34.AoS4.3
continuous random variables:
- construction of probability density functions from non-negative functions of a real variable
- specification of probability distributions for continuous random variables using probability density functions
- calculation and interpretation of mean, 𝜇, variance, 𝜎^2, and standard deviation of a continuous random variable and their use
- standard normal distribution, N(0, 1), and transformed normal distributions, N(𝜇, 𝜎^2), as examples of a probability distribution for a continuous random variable
- effect of variation in the value(s) of defining parameters on the graph of a given probability density function for a continuous random variable
- calculation of probabilities for intervals defined in terms of a random variable, including conditional probability (the cumulative distribution function may be used but is not required)
