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How do you find a probability of a range?
First, we calculate P(X ≤ b) and then subtract P(X ≤ a). The graph below helps illustrate this situation. Thus, we are able to calculate the probability for any range of values for a normal distribution using a standard distribution table.
What is average probability?
If you have a collection of numbers a1,a2,…,aN, their average is a single number that describes the whole collection. We would like to define its average, or as it is called in probability, its expected value or mean. The expected value is defined as the weighted average of the values in the range.
How to calculate probability in a given range?
Examples, videos, solutions, activities and worksheets that are suitable for A Level Maths to help students learn how to work out a probability in a given range. There are four tutorials in this series which show you how to work out a probability in a given range.
How to define the expected value of X?
Now, consider a random variable X. We would like to define its average, or as it is called in probability, its expected value or mean. The expected value is defined as the weighted average of the values in the range. Let X be a discrete random variable with range RX = {x1, x2, x3,… } (finite or countably infinite).
Which is an example of an average number?
If you have a collection of numbers a1, a2,…, aN, their average is a single number that describes the whole collection. Now, consider a random variable X. We would like to define its average, or as it is called in probability, its expected value or mean.
How to calculate the expected value of a random variable?
The following theorem states that expectation is linear, which makes it easier to calculate the expected value of linear functions of random variables. E [ X 1 + X 2 + ⋯ + X n] = E X 1 + E X 2 + ⋯ + E X n, for any set of random variables X 1, X 2, ⋯, X n.