Tutorial on Discrete Probability Distributions
Tutorial on discrete probability distributions 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 discrete probability distribution consists of the values of the random variable X and their corresponding probabilities P(X).
The probabilities P(X) are such that ∑ P(X) = 1Example 1:Let the random variable X represents the number of boys in a family.
a) Construct the probability distribution for a family of two children.
b) Find the mean and standard deviation of X.Solution to Example 1: * a) We first construct a tree diagram to represent all possible distributions of boys and girls in the family. * Assuming that all the above possibilities are equally likely, the probabilities are:
P(X=2) = P(BB) = 1 / 4
P(X=1) = P(BG) + P(GB) = 1 / 4 + 1 / 4 = 1 / 2
P(X=0) = P(GG) = 1 / 4 * The discrete probability distribution of X is given by X P(X) 0 1 / 4
1 1 / 2
2 1 / 4
* * Note that ∑ P(X) = 1 * b) The mean µ of the random variable X is defined by µ = ∑ X P(X)
= 0 * (1/4) + 1 * (1/2) + 2 * (1/4) = 1 * The standard deviation σ of the random variable X is defined by σ = Square Root [ ∑ (X µ) 2 P(X) ]
= 1 / square root (2)Example 2:Two balanced dice are rolled. Let X be the sum of the two dice.
a) Obtain the probability distribution of X.
b) Find the mean and standard deviation of X.Solution to Example 2: * a) When the two balanced dice are rolled, there are 36 equally likely possible outcomes as shown below . * The possible values of X are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. * The possible outcomes are equally...
...
_____
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...
...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...
...Discrete and Continuous Probability
All probabilitydistributions can be categorized as discreteprobabilitydistributions or as continuous probabilitydistributions (stattrek.com). A random variable is represented by “x” and it is the result of the discrete or continuous probability. A discrete...
...TEM1116 Probability and Statistics
Tri1 2013/14
Chapter 1
Chapter 1: Discrete and Continuous ProbabilityDistributions
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
1...
...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?...
...2800
c. 1.75
d. 784
12. If a six sided die is tossed two times and “3” shows up both times, the probability of “3” on the third trial is
a. much larger than any other outcome
b. much smaller than any other outcome
c. 1/6
d. 1/216
13. If P(A) = 0.4, P(B A) = 0.35, P(A B) =0.69, then P(B) =
a. 0.14
b. 0.43
c. 0.75
d. 0.59
14. Two events with nonzero probabilities
a. can be both mutually exclusive and independent
b. can not be...
...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...
...QMT200
CHAPTER 3: PROBABILITYDISTRIBUTION
3.1
RANDOM VARIABLES AND PROBABILITYDISTRIBUTION
Random variables is a quantity resulting from an experiment that, by chance, can assume different values. Examples of random variables are the number of defective light bulbs produced during the week and the heights of the students is a class. Two types of random variables are discrete random variables and continuous...
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