Discrete and Continuous Probability
All probability distributions can be categorized as discrete probability distributions or as continuous probability distributions (stattrek.com). A random variable is represented by “x” and it is the result of the discrete or continuous probability. A discrete probability is a random variable that can either be a finite or infinite of countable numbers. For example, the number of people who are online at the same time taking a statistics class at CTU on a given day is a discrete random probability. Another example of a discrete random probability is the number of people who stand in a checkout lane in Kroger on a given day. A continuous probability is a random variable that is infinite and the number is uncountable. An example of a continuous probability is the wait time in a Kroger line on a given day and time and that number could be 5 minutes, 5.2 minutes, or 5.34968...minutes. The same can be said if the example was the amount of silk a silk worm produced on a given day. The dice experiment is a discrete random probability because it yielded 6 possible outcomes which are 1, 2, 3, 4, 5, and 6. The number that the die landed on after each roll is “x” or the random variable. The discrete random probability is a countable number because the dice only has 6 sides. The experiment produced three 1’s, four 2’s, five 3’s, two 4’s, four 5’s and two 6’s. The experiment is a probability distribution because all six sides had the same “chance” to land on its side under the “set” conditions of 20 rolls. This is not a binomial probability because it has more than two possible outcomes. The outcome of the die has 6 possibilities or a 1 out of 6 chance to land on its side which would disqualify it as binomial. A binomial probability only deals with successes or failures. This type of experiment either does something or it doesn’t, there is no in between. References
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1. What is mean, variance and expectations?
Mean  The mean of a discrete random variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations, which gives each observation equal weight, the mean of a random variable weights each outcome xi according to its probability, pi. The mean also of a random variable provides the longrun average of the variable, or...
...Tutorial on DiscreteProbabilityDistributions
Tutorial on discreteprobabilitydistributions with examples and detailed solutions.

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 Let X be a random variable that takes the numerical values X1, X2, ..., Xn with probablities p(X1), p(X2), ..., p(Xn) respectively. A...
...TEM1116 Probability and Statistics
Tri1 2013/14
Chapter 1
Chapter 1: Discrete and ContinuousProbabilityDistributions
Section 1: Probability
Contents: 1.1 1.2 1.3 1.4 1.5 Some basics of probability theory Axioms, Interpretations, and Properties of Probability Counting Techniques and Probability Conditional Probability Independence
TEM1116...
...Statistics
Chapter 5
Some Important DiscreteProbabilityDistributions
51
Chapter Goals
After completing this chapter, you should be able
to:
Interpret the mean and standard deviation for a
discreteprobabilitydistribution
Explain covariance and its application in finance
Use the binomial probabilitydistribution to find
probabilities
Describe when to...
...Probabilitydistribution
Definition with example:
The total set of all the probabilities of a random variable to attain all the possible values. Let me give an example. We toss a coin 3 times and try to find what the probability of obtaining head is? Here the event of getting head is known as the random variable. Now what are the possible values of the random variable, i.e. what is the possible number of times that head might occur?...
...EXERCISES (DiscreteProbabilityDistribution)
EXERCISES (DiscreteProbabilityDistribution)
P X x n C x p 1 p
x
BINOMIAL DISTRIBUTION
n x
P X x n C x p 1 p
x
BINOMIAL DISTRIBUTION
n x
1. 2. 3.
The probability that a certain kind of component will survive a given shock test is ¾. Find the...
...The Poisson probabilitydistribution, named after the French mathematician SiméonDenis. Poisson is another important probabilitydistribution of a discrete random variable that has a large number of applications. Suppose a washing machine in a Laundromat breaks down an average of three times a month. We may want to find the probability of exactly two breakdowns during the next month. This is an example of a...
...ProbabilityDistribution Essay
Example Suppose you flip a coin two times. This simple statistical experiment can have four possible outcomes: HH, HT, TH, and TT. Now, let the random variable X represent the number of Heads that result from this experiment. The random variable X can only take on the values 0, 1, or 2, so it is a discrete random variable
Binomial Probability Function: it is a discrete...
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