Essay on Probability Theory and Random Variable

Words: 964
Pages: 4
Open Document
Event A is rolling a die and getting a 6. Suggest another event (Event B) that would be independent from Event A.
A company runs 3 servers, each providing services to 40 computers. For each server, two of its client 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 with Event A. What is the probability of getting 6 tails in 10 …show more content…
Find the math expectation of Ryan’s winnings after 3 games.
Find the variance of Ryan’s winnings for a single game.
Find the standard deviation of Ryan’s winnings for a single game.
Does it pay for Ryan to play this game at the fair? Explain.
Find the cumulative distribution function of Ryan’s winnings for a single game and draw its graph.
(5 points each for parts a-e and 20 points for part f)
X -$5 $0 $10 $50
P 0.60 0.20 0.10 0.10
Find , , if a random variable is given by its density function, such that(25 points) QUOTE , if QUOTE QUOTE , if QUOTE QUOTE , if QUOTE Let be given by its distribution function , such that QUOTE , if QUOTE (25 points) QUOTE , if QUOTE QUOTE , if QUOTE
Graph the distribution function
Graph the density function
Find ,,
A random variable is distributed normally with QUOTE and QUOTE . Find P(3≤X<4.5). The distribution of the length of a standard piece of computer paper is normal with an expectation of 11 inches and the standard deviation of 0.1 inch.
Find the probability that the length of any given piece of computer paper is between 10.95 and 11.10.
Find the probability that the length of any given piece of computer paper is less than 10.90.
Find the probability that the length of any given piece of computer paper is greater than 11.20.
The density function of a random variable is given by

Find its (a) math expectation, (b) variance and (c)
Show More

Related Documents: Essay on Probability Theory and Random Variable

Six Sigma5 Essay

Probability and Statistics Basic Probability concepts Most inspection and quality control theory deals with statistics to make inference about a population based on information contained in samples. The mechanism we use to make these inferences is probability. We use P E to represent the probability of any event (E) 0 PE 1 The sum of all possible events = 1 P(S) = 1, S = Sample space Definition of Probability The ratio of the chances favoring an event to the total number of chances for and against…

Words 2846 - Pages 12

AP Stats Vocab List 2 Essay

A.P. Statistics – Vocabulary List Add your own definitions and examples or references, as are appropriate, to the following vocabulary. (Please note: These lists may be collected on a random basis for credit.) Vocabulary Term Definition, Examples, References table a set of data arranged in rows and columns 表格 68-95-99.7 Rule In statistics, the 68–95–99.7 rule, also known as the three-sigma rule or empirical rule, states that nearly all values lie within three standard deviations of the mean…

Words 7770 - Pages 32

Randomness Definition

Randomness means different things in various fields. Commonly, it means lack of pattern or predictability in events. The Oxford English Dictionary defines "random" as "Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard." This concept of randomness suggests a non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination. Applied usage…

Words 480 - Pages 2

What Is Social Scientific Inquiry?

there a problem? Why is there a change in scope Variables – logic, empiricism, objectivity, control cyclical – logic: theoretical sense (can’t change what you’re observing to be a better fit). Empiricism – using all your senses – practical – relying on senses. Objectivity – rid of any bias – see the world the way it is. Control – set limit on research to control factors to avoid bias. Cyclical – TR – relationship between theory and research variable in a shisha is ccoel Nomothetic and ideographic…

Words 887 - Pages 4

Prison: Scientific Method and Larger Population Essay

CJ 540 Midterm Case study (life history) – in-depth investigation of a single case (individual, group, or community). Concepts – abstract or symbolic tags placed on reality. Control variable - third variable introduced to test the relationship between the independent and dependent variables. Cost-effectiveness - cost to achieve goals, outcomes (e.g. cost to reduce drug use among treatment program participants). Cost-efficiency - cost per unit of work (e.g. cost to make an arrest)…

Words 995 - Pages 4

Probality and probality distributions Essay

Chapter 4 Probability and Probability Distributions Classical Interpretation (Way 1) This interpretation of probability arose from games of chance. Common sense and theory tell us that: - The probability of a HEADS from a fair coin is ½ - The probability of an ACE is 4/52 or 1/13 1 - The probability of a SEVEN on two dice is 6/36 or 1/6 First die: Second die: 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 4 5 6 7 5 6 7 8 6 7 8 9 7 8 9 10 8 9 10 11…

Words 7500 - Pages 30

Essay about Econometrics: Regression Analysis and Ceteris Paribus Effect

relationship between two variables. - If variables are related they are correlated - Economic theory informative about sign or range, but uninformative about magnitude - Regression analysis allows the quantification of relationships posited by economic theory Y = Dependent variable, the explained variable, the response variable, the predicted variable or the regressand X = Independent variable, the explanatory variable, the control variable, the predictor variable or the regressor…

Words 1015 - Pages 5

Essay about Christopher Sims Monetary Policy And It

disciplines, it is easy to find economists of high reputation who disagree strongly with one another on issues of wide public interest. This may suggest that economics, unlike most other scientific disciplines, does not really make progress. Its theories and results seem to come and go, always in hot dispute, rather than improving over time so as to build an increasing body of knowledge. There is some truth to this view; there are examples where disputes of earlier decades have been not so much resolved…

Words 9146 - Pages 37

Computers And Chemical Engineering 26 2002 Essay

distribution of the demand, explore its connection with the corresponding Markov chains, and integrate these into our decision making. In particular, we formulate the Markov decision model by identifying the chain’s state space and the transition probabilities, specify the cost structure and evaluate its individual component; and then use the policy-improvement algorithm to obtain the optimal policy. Application examples are provided for illustration. © 2002 Elsevier Science Ltd. All rights reserved…

Words 8274 - Pages 34

Essay on Tute Week 8 exercises answers 1

usefulness of probability in the real world. Introduction – Do critical thinkers need probability theory? Out in the real world, trillions of events that depend upon random chance are occurring every second. A die is rolled, the gender of a child is determined, a plane crashes or an election is won. The word ‘probability’, refers to the likelihood of such events taking place. More generally, probability theory provides us with tools for studying, measuring and summarising probabilities associated with…

Words 2406 - Pages 10