Please use your calculators and give your ﬁnal answers to 3 signiﬁcant ﬁgures. Show your work for full credit. Please state clearly all assumptions made.
1. Classify each random variable as discrete or continuous. (a) The number of visitors to the Museum of Science in Boston on a randomly selected day. (b) The camberangle adjustment necessary for a frontend alignment. (c) The total number of pixels in a photograph produced by a digital camera. (d) The number of days until a rose begins to wilt after it is purchased from a ﬂower shop. (e) The runnning time for the latest James Bond movie. (f) The blood alcohol level of the next person arrested for DUI in a particular county. 2. A bagel shop sells only two diﬀerent types of bagels: plain (P) and cinnamon raisin (C). Five customers are selected at random. Past records have shown that the demand for cinnamon bagels is twice that for plain bagels. Each customer buys only one bagel and the experiment consists of recording what kind of bagel these ﬁve customers buy. Let the random variable X be the number of people who buy a plain bagel. (a) Find the probability distribution for X. (b) Suppose at least 3 people buy a plain bagel. What is the probability that exactly 4 people buy a plain bagel? 3. The probability distribution for a discrete random variable X is given by the formula p(r) = for r = 1, 2, . . . , 6. (a) Verify that this is a valid probability distribution. (b) Find P (X = 4). (c) Find P (X > 2). (d) Find the probability that X takes on the value 3 or 4. (e) Construct the corresponding probability histogram. 4. Two packages are independently shipped from Fort Collins, Colorado, to the same address in Seattle, Washington, and each is guaranteed to arrive within 4 days. The probability that a package arrives within 1 day is 0.10, within 2 days is 0.15, within 3 days is 0.25, and on the fourth day is 0.50. Let the random variable X be the total...
...What is mean, variance and expectations?
Mean  The mean of a discrete randomvariable X is a weighted average of the possible values that the randomvariable can take. Unlike the sample mean of a group of observations, which gives each observation equal weight, the mean of a randomvariable weights each outcome xi according to its probability, pi. The mean also of a random...
...infected. What is the probability that 3 randomly chosen client computers serviced by different servers (one per server) will all be infected?
The probability that Alice’s RSA signature on a document is forged is () What is the probability that out of 4 messages sent by Alice to Bob at least one is not forged?
Event A is selecting a “red” card from a standard deck at random. Suggest another event (Event B) that is compatible...
...Chapter 3 ProbabilityDistributions
1. Based on recent records, the manager of a car painting center has determined the following probabilitydistribution for the number of customers per day. Suppose the center has the capacity to serve two customers per day.
x P(X = x) 
0 0.05 
1 0.20 
2 0.30 
3 0.25 
4 0.15 
5...
...Probabilitydistribution
Definition with example:
The total set of all the probabilities of a randomvariable 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 randomvariable. Now what are the possible values of the random...
...Important Discrete
ProbabilityDistributions
51
Chapter Goals
After completing this chapter, you should be able
to:
Interpret the mean and standard deviation for a
discrete probabilitydistribution
Explain covariance and its application in finance
Use the binomial probabilitydistribution to find
probabilities
Describe when to apply the binomial distribution
Use...
...Tutorial on Discrete ProbabilityDistributions
Tutorial on discrete probabilitydistributions with examples and detailed solutions.

Top of Form

Web  www.analyzemath.com 

Bottom of Form 
 Let X be a randomvariable that takes the numerical values X1, X2, ..., Xn with probablities p(X1), p(X2), ..., p(Xn) respectively. A discrete...
...THE MOMENTS OF A RANDOMVARIABLE
Definition: Let X be a rv with the range space Rx and let c be any known constant. Then the kth moment of X about the constant c is defined as
Mk (X) = E[ (X c)k ]. (12)
In the field of statistics only 2 values of c are of interest: c = 0 and c = . Moments about c = 0 are called origin moments and are denoted by k, i.e., k = E(Xk ), where c = 0 has been inserted...
...MULTIPLE CHOICE QUESTIONS (50%)
1. Temperature is an example of a variable that uses
a. the ratio scale
b. the interval scale
c. the ordinal scale
d. either the ratio or the ordinal scale
2. The nominal scale of measurement has the properties of the
a. ordinal scale
b. only interval scale
c. ratio scale
d. None of these alternatives is correct.
3. Statistical studies in which researchers control variables of interest are
a. experimental...
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