ANSWER THE FOLLOWING QUESTIONS. SHOW YOUR SOLUTIONS AND ENCIRCLE YOUR FINAL ANSWERS. SUBMIT THIS ON WEDNESDAY.
1. Suppose that the likelihood that someone who logs into a particular site in a shopping mall on the web will purchase an item is .20. If the site has 10 people accessing it in the next minute, what is the probability that a) Exactly 2 individuals will purchase an item?
b) At least 2 individuals will purchase an item?
c) At most 2 individuals will purchase an item?
2. The quality Control Manager of ATV Cookies is inspecting a batch of chocolatechip cookies that has been baked. If the production process is in control, the average number of chip parts per cookie is 6. What is the probability that in any particular cookie being inspected a) Exactly five chip parts will be found?
b) Fewer than five chip parts will be found?
c) Five or more chip parts will be found?
3. An important part of the customer service responsibilities of a telephone company relate to the speed with which troubles in residential service can be repaired. Suppose past data indicate that the likelihood is .70 that troubles in residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that a) All five will be repaired on the same day?
b) At least three will be repaired on the same day?
c) Fewer than two will be repaired on the same day?
4. A state lottery is conducted in which six winning numbers are selected from a total of 54 numbers. What is the probability that if six numbers are randomly selected a) All six numbers will be winning numbers?
b) Four numbers will be winning numbers?
c) None of the numbers will be winning numbers?
5. The average number of claims per hour made to the Philam Insurance company for disabilities and death is 3.1. what is the probability that in any given hour a) Fewer than three...
...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 the expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is , formally defined by
Variance  The variance of a discrete random variable X measures the spread, or variability, of the distribution, and is defined by
The standard deviation is the square root of the variance.
Expectation  The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring. The expected value of X is usually written as E(X) or m.
E(X) = S x P(X = x)
So the expected value is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)].In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on average.
2. Define the following;
a) Binomial Distribution  is the discreteprobability distribution of the number...
...Tutorial on DiscreteProbability Distributions
Tutorial on discreteprobability distributions with examples and detailed solutions.

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Web  www.analyzemath.com 

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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 discreteprobability 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 discreteprobability 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)...
...PROBABILITY and MENDELIAN GENETICS LAB
Hypothesis: If we toss the coin(s) for many times, then we will have more chances to reach the prediction that we expect based on the principle of probability.
Results:
As for part 1: probability of the occurrence of a single event, the deviation of heads and tails of 20 tosses is zero, which means that the possibility of heads and tails is ten to ten, which means equally chances. The deviation of heads and tails of 30 tosses is 4, which means that the occurrence of head is 19 and the occurrence of tail is 11. The deviation of heads and tails of 50 tosses is 3, which means that the occurrence of head is 28 and the occurrence of tail is 22. Compare the second and third observation, we can find that the deviation decrease one. It is corresponding to the hypothesis. The more times we use to toss the coin, the more opportunities we will get to reach the prediction based on the principle of probability.
As for part 2: probability of independent events occurring simultaneously, the observation of HeadsHeads is 11, which is 27.5% of the total experiment. And the deviation is 1. The observation of HeadsTails or TailHeads is 16, which is 40% of the total. And the deviation is 4. The observation of Tails Tails is 13, which is 32.5% of the total number. And the deviation is 3.
Discussion:
In this lab, we’d learn about the likelihood that a particular event will...
...CHAPTER 3: PROBABILITY DISTRIBUTION
3.1
RANDOM VARIABLES AND PROBABILITY DISTRIBUTION
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 random variable.
3.2DISCRETE RANDOM VARIABLE
A random variable is called a discrete random variable if its set of posibble outcomes is countable. Probability distribution is a listing of all the outcomes of an experiment and the probability associated with each outcome. For example, the probability distribution of rolling a die once is as below: Outcome, x Probability, P(x) 1 1 6 2 1 6 3 1 6 4 1 6 5 1 6 6 1 6
The probability distribution for P(x) for a discrete random variable must satisfy two properties: 1. The values for the probabilities must be from 0 to 1; 0 ≤ ( ) ≤ 1 2. The sum for P(x) must be equal to 1; ∑ ( ) = 1
QMT200
3.2.1 FINDING MEAN AND VARIANCE Mean of X is also referred to as its “expected value”.
= ( ) Where: = ∑[ ( )]
( )=
= (
) − [ ( )]
(
)=
[
( )] = ( )
Example 1 An experiment consists of tossing two coins simultaneously. Write down...
...Learning Programmes Division
Second Semester 20102011
Course Handout
Course Number
Course Title
: AAOC ZC111
: Probability and Statistics
Course Email address : aaoczc111@dlpd.bitspilani.ac.in
Course Description
Probability spaces; conditional probability and independence; random variables and probability
distributions; marginal and conditional distributions; independent random variables, mathematical
exceptions, mean and variance, Binomial Poisson and normal distribution; sum of independent random
variables; law of large numbers; central limit theorem; sampling distributions; tests for mean using normal
and student’s distributions; tests of hypotheses; correlation and linear regression.
Scope and Objectives
At the end of the course, the student should be able to understand probabilistic & deterministic models and
statistical inference and apply these concepts to solve a variety of problems.
Prescribed Text Book
T1
Johnson Richard A. & C.B. Gupta, Miller & Freund’s Probability and Statistics for Engineers, PHI,
7th Ed., 2005.
Reference Books
R1.
Paul L. Meyer, Introductory Probability and Statistical Appl., Second Edition. AddisonWesley, 1970.
R2. M.S. Radhakrishnan, Probability & Statistics, DLPD Notes Note: Softcopy of this Supplementary notes will
be available for download from BITS DLP website.
R3. Mendenhall Beaver Beaver, Introduction to...
...Decision Analysis
Course Outline, Quarter I, 2006
Class Materials Topic
Hardcopy in Packet Other*
Introduction
1 Freemark Abbey Winery Structuring Decisions
Framework for Analyzing Risk
2 The North Star Concert North Star.xls Best Guess, Worst Case, Best Case; and Continuous Uncertainties
3 Engine Services, Inc.
Quick Start Guide to Crystal Ball
Analyzing Uncertainty, Probability Distributions, and Simulation Learning Module: Crystal Ball Litigate Demo
Engine Services.xls Language of Probability Distributions and Monte Carlo Simulation
4 Taurus Telecommunications Corporation: A New Prepaid Phone Card Learning Module: Tornado Sensitivity
Taurus Telecommunications.xls Sensitivity Analysis and Key Drivers
Time Value of Money
5 Dhahran Roads (A)
Evaluating Multiperiod Performance Multiperiod Pro Forma and NPV
6 Roadway Construction Company NPV, IRR, and Project Assumptions
Data and Distributions
7 Appshop, Inc. Simulating NPV
8 Lorex Pharmaceuticals
Introduction to Analytical Probability Distributions Lorex Exhibit 2.xls Distributions
9 Sprigg Lane (A) Sprigg2.xls Probability Distributions and Spreadsheet Modeling; Risk
10 The Waldorf Property
Chapter 11 of QBA: Text and Cases
Waldorf.xls Cumulative Distribution Functions, Adjustment for Risk
11 Amore Frozen Foods (A) Macaroni and Cheese Fill Targets
Sampling Amore.xls Sample Uncertainty
Regression
12 Hightower Department Stores:...
...PROBABILITY DISTRIBUTION
In the world of statistics, we are introduced to the concept of probability. On page 146 of our text, it defines probability as "a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur" (Lind, 2012). When we think about how much this concept pops up within our daily lives, we might be shocked to find the results. Oftentimes, we do not think in these terms, but imagine what the probability of us getting behind the wheel of a car twice a day, Monday through Friday, and arriving at work and home safely. Thankfully, the probability for me has been 'one'! This means that up to this point I have made it to work and returned home every day without getting into an accident. While probability might have one outcome with one set of circumstances, this does not mean it will always turn out that way. Using the same example, just because I have arrived at work every day without getting into an accident, this does not mean it will always be true. As I confess with my words, and pray it does stay the same, probability tells me there is room for a different outcome.
In business, we often look at the probability of success or financial gain when making a decision. There are several things to take into consideration such as the experiment, potential outcomes, and possible events. An...
...pairs of shoes. Five shoes are drawn at random. What is the probability that at least one pair of shoes is obtained? 2. At a camera factory, an inspector checks 20 cameras and ﬁnds that three of them need adjustment before they can be shipped. Another employee carelessly mixes the cameras up so that no one knows which is which. Thus, the inspector must recheck the cameras one at a time until he locates all the bad ones. (a) What is the probability that no more than 17 cameras need to be rechecked? (b) What is the probability that exactly 17 must be rechecked? 3. We consider permutations of the string ”ABACADAFAG”. How many permutations are there? How many of them don’t have any A next to other A? How many of them have at least two A’s next to each other? 4. A monkey is typing random numerical strings of length 7 using the digits 1 through 9 (not 0). Call the digits 1, 2, and 3 ”lows”, call the digits 4, 5, and 6 ”mids” and digits 7, 8 and 9 ”highs”. (a) How many diﬀerent strings can he type? (b) How many of these strings have no mids? (c) How many of these strings have only one high in them? For example, the string 1111199 has two highs in it. (d) What’s the probability that a string starts with a low and ends with a high? (e) What’s the probability that a string starts with a low or ends with a high? (f) What’s the probability that a string doesn’t have at least one of the digits 1 through...