5.2 Probability distribution for discrete random variable
What is a random variable?
A numerical characteristic that takes on different values due to chance
Every single time we flip a coin, the number of heads is a random variable because the results will vary between trials.
Sample of 100 are pulled from the population and their heights are measured. Mean height is a random variable because the statistic will vary between samples.
Classified into two broad types: Discrete and continuous
Discrete: Countable set of distinct possible values; It allows us to look at measures based on differences (fixed/constant unit)
Example: Number of heads in 4 flips of a coin
Continuous: Any value (to any number of decimal places) within some interval is a possible value
Example: Time to finish a test
Probability distribution (0?P?1)
For a discrete random variable, its probably distribution is any table, graph, or formula that gives each possible value and the probability of that value
Suppose a random variable X may take k different values, with the probability that X = xi defined to be P(X = xi) = pi. The probabilities pi must satisfy the following:
2: mmation is over all possible values taken by the random variable
Test 1 Time - START FINISH
1. In the random experiment of tossing two fair coins where the random variable is the number of heads observed, we have
Value of X
2. In an examination paper, there are three multiple choice questions, for each which only one of the five given answers is correct. A student receives four marks for a correct answer and loses one mark for an incorrect answer. If the student guesses the answer to each question, then for each question the probability of given the correct answer is 1/5 and the probability of giving an incorrect answer is 4/5. Representing the correct answer by C and an incorrect (wrong) answer by W, the eight outcomes in the sample space, and the probabilities of these outcomes are:
The probability distribution of the random variable, X, the number of correct answers, is:
The probability distribution of the random variable, Y, the number of marks scored by the student, is:
5.3 Binomial distribution
What is involved in binomial distribution?
Binomial Experiment (statistical experiment):
? The experiment consists of n repeated trials
? Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, failure
? The probability of success, denoted by P, is the same on every trial
? The trials are independent; that is, the outcome on one trial does not...