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What is an equation to show the sum of all the probablilites is equal to 1?
The equation is Integral of p(x), where p(x) is the probability distribution function, and x ranges over its whole domain. For a discrete variable, the integral would be replaced by summation.
For a continuous random variable the probability that the value of x is greater than a given constant is?
The integral of the density function from the given point upwards.
What is the difference between sigma and integral?
Sigma is a discrete sum, a sum with steps. Eg. add the numbers from 1 to 10 or add the numbers 1/2, 1/4,... A sigma always has a concept of a next thing to add, even if the list of things goes on forever. An integral is a continuous summation. It is a summation in that we are adding up the area under the curve, for example, but it is continuous in that because we are adding things of arbitrary smallness it's not really possible to always point to the individual terms that are being added because they become some kind of continuous blur. Instead we use some mathematical technique (integration). But still it is a kind of summation.
What do you do if a particular integral you want to evaluate is not listed in the table?
Two main options.Carry out numerical integration - there are various methods - the trapezium method being one of the simpler ones; orfind two integrable functions such that one is greater than the given function and the other is smaller than it. Then your integral will lie between the integrals of these two functions.
Other words for addition in maths?
Sum or summation
