SS3 First Term Further Mathematics Lesson Note – Probability Distribution and Approximations

The content is just an excerpt from the complete note for SS3 First Term Further Mathematics Lesson Note – Probability Distribution and Approximations. Check below to download the complete DOCUMENT

WEEK 8

TOPIC: – Probability distribution and Approximations

Content:

1. Binomial approximations by Poisson distributions
2. Poisson distribution
3. Normal distributions and Normal approximations
4. Binomial approximations by Poisson distributions

Binomial Distributions

In our last discussion in sss2, we leant about concept of probability and calculated probability and events.

We want to see how to find probabilities of different values of discrete variables such as counts scores.

Probability Distributions: – Certain natural occurrences have characteristic random behaviours. When theoretical probability model or distribution is built on their nature of randomness, we say such a model or theoretical distribution is called a probability distribution.

Mathematically this is defined: – when a random variable x can assume a discrete set of values x₁,x₂,………x_k with probability p₁,p₂,p₃…….p_k where  then we say that a probability function of x written as p(x), is defined.

Remember the binomial expression, the binomial probability lings round the binomial theorem. Consider repeated and independent trials of an experiment with two possible outcomes, one of the outcome is called success and the other failure. Let P be the probability of success then

q=1-p is probability of failure. The interest is in number of successes not the order they occur when n numbers of trials are made and x is numbers of successes, then the binomial distribution is given by

To gain full access to the note: DOWNLOAD FILE