A random variable assigns a number to each outcome of a random circumstance, or, equivalently, a random variable assigns a number to each unit in a population. It is easier to create rules for broad classes of situations and then identify how a specific example fits into a class than it is to create rules for each specific example. We can employ this strategy quite effectively for working with a wide variety of situations Involving probability and random outcomes. We categorize these situations by defining a generic numerical outcome, or "random variable." for similar random circumstances. Identifying the type of random variable ap¬propriate in a given situation makes it easy to find probabilities and other infor¬mation that would be difficult to derive from first principles. There are two different broad classes of random variables:

1.A continuous random variable can take any value in an interval or col¬lection of intervals. 2.A discrete random variable can take one of a countable list of distinct values.

Sometimes a random variable fits the technical definition of a dis¬crete random variable but it is more convenient to treat it as a continuous random variable. Examples include Incomes, prices, and exam scores. Sometimes continuous random variables are rounded off to whole units, giving the appearance of a discrete random variable, such as age in years or pulse rate to the nearest beat. In most of these situations, the num¬ber of possible values is large and we are more interested in probabilities concerning intervals than specific values, so the methods for continuous random variables will be used. We can consider discrete and continuous random variables separately because probabilities are computed and used differently for them. For discrete random variables, we are interested in probabilities of exact outcomes or a series of them. For continuous random variables, we are Interested in the probability of the outcome...

...SIDS31081 - Statistics Refresher
2006 – 2007
Exercises
(Probability and RandomVariables)
Exercise 1
Suppose that we have a sample space with five equally likely experimental outcomes :
E1,E2,E3,E4,E5.
Let
A = {E1,E2}
B = {E3,E4}
C = {E2,E3,E5}
a. Find P(A), P(B), P(C).
b. Find P(A U B) . Are A and B mutually exclusive?
c. Find Ac, Bc, P(Ac), P(Bc).
d. Find A U Bc and P(A U Bc)
e. Find P(B U C)
Exercise 2
A committee with two members is to be...

...depression are five times more likely to have a breathing- related sleep disorder than people who are not depressed.
Depression and Breathing-related sleep disorders; Dependant
3. A horse race has 10 entries. Assuming that there are no ties, what is the probability that the three horses owned by one person finish first second, and third?
The number of possible combinations of 3 horses winning, in any order, is
So the probability is
4. In how many...

...computers are 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...

...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...

...continuous randomvariable because the time is being measured. All possible results for the variable time (t) would be greater than > 0.
b) The weight of a T-bone steak is a continuous randomvariable because the weight of the steak is measured. All the possible results for the weight of the T-bone steak would be positive numbers making the variable weight (w) > greater than 0....

...0.3 or take a loss of $1000 with probability 0.7. What is this person’s expected gain?
4.10 Two tire-quality experts examine stacks of tires and assign a quality rating to each tire on a 3-point
scale. Let X denote the rating given by expert A and Y denote the rating given by B. The following table
gives the joint distribution for X and Y .
4.12 If a dealer’s proﬁt, in units of $5000, on a new automobile can be looked upon as a randomvariable
X...

...APStatistics Cole Rogers
Unit 7 Exam RandomVariables: Free Response
Directions: Complete the assignment on this paper. If you need additional paper make sure that you clearly label each page with your name. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit.
1. A Roulette wheel has 38 slots numbered 0 to 36 and 00. The wheel is spun and a ball is thrown into the wheel and comes to...

...fructose
Answer the following questions using the images supplied.
a) What type of polymer is being illustrated in the diagram and what is the evidence that lead to your decision? (2 marks)
b) Label the two types of bonds illustrated in the diagram. (2 marks)
c) What two types of structures of this polymer are being shown in the diagram? To support your...

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