HSC Together Year 11 Maths Advanced: Expected Value, Variance, and Standard Deviation

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# Expected Value, Variance, and Standard Deviation

### What is expected value, variance and standard deviation?

In this post, we use discrete random variables and associated probabilities to solve practical problems, as a part of the Prelim Maths Advanced course under the topic Statistical Analysis and sub-part Discrete Probability Distributions, specifically focusing on expected value, variance and standard deviation. We:

• Use relative frequencies obtained from data to obtain point estimates of probabilities associated with a discrete random variable
• Recognise uniform discrete random variables and use them to model random phenomena with equally likely outcomes
• Examine simple examples of non-uniform discrete random variables, and recognise that for any random variable, X , the sum of the probabilities is 1
• Recognise the mean or expected value, E(X) = \mu , of a discrete random variable X as a measure of centre, and evaluate it in simple cases
• Recognise the variance, Var(), and standard deviation ( \sigma ) of a discrete random variable as measures of spread, and evaluate them in simple cases
• Use Var(X) = E((X - \mu)^{2}) = E(X^{2})  -  \mu^{2} for a random variable and Var(x) = \sigma^{2} for a dataset.

### What is expected value?

The following two videos will introduce you to expected values E(X) , and how to approach and set-out the calculations.

### What is variance?

The following two videos will introduce you to variance, and how to set-out the required calculations.

### What is standard deviation?

The following two videos will introduce you to standard deviation, and how to go about visualising and calculating it.

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