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BSTAT 5301 T2
Test 2
| Question | Answer |
|---|---|
| With respect to events, probability vs statistics? | Probability deals with predicting the likelihood of future events, while Statistics involves in analyzing the frequency of past events. |
| With respect to mathematics, probability vs statistics? | Probability is primarily a theoretical branch of mathematics. Statistics is primarily an applied branch of mathematics, which tries to make sense of observations in the real world. |
| How does probability law and statics relate? | Probability Laws will still hold good without Statistics. We need Statistics to find the numerical values of the Probabilities. |
| What is probability? | Probability (in simple terms) is the likelihood of occurrence of an event. |
| What is an event? | The event, in general, is observed in a statistical Experiment. The Event is a set of Outcomes in an Experiment. An Event is a collection of one or more simple events |
| What is an experiment? | An experiment is any process of observation with an uncertain outcome. Refers to "performing a controlled experiment" or "observing uncontrolled events" |
| What are experimental outcomes? | The unique outcomes for an experiment are called the experimental outcomes |
| What is sample Space? | The sample space of an experiment is the set of all possible experimental outcomes. |
| What is a simple event? | A Simple Event is a single outcome of an experiment. |
| The probabilities of all the experimental outcomes must sum to? | 1 |
| What are the three approaches to find Probabilities? | Classical method, Relative Frequency method, and Subjective Method. |
| What is the Classical approach to finding probabilities? | Based on equally likely outcomes |
| What is the Relative frequency approach to finding probabilities? | Using the long run relative frequency – based on History or Experimental data |
| What is the Subjective approach to finding probabilities? | Assessment based on experience, expertise or intuition |
| Requirements for Classical approach? | Outcomes must be mutually exclusive, exhaustive. If an experiment has n possible outcomes, the probability each outcome is 1/n |
| What are the combinations and relationships between events? | "Complement event Intersection of events Union of events Mutually exclusive events Dependent and independent events" |
| What are the methods for determining probabilities of events that result from combining other events? | Joint, Marginal, and Conditional Probability |
| What is the complement of an event? | The complement of event A is defined to be the event consisting of all sample points that are “not in A”. |
| What is a union? | The union of A and B are elementary events that belong to either A or B or both. For probability denoted as P(A or B) |
| What is an intersection? | The intersection of A and B are elementary events that belong to both A and B. For probability denoted as P(A and B). Or the joint probability. |
| Probability Rules | "The Addition Rule The Complement Rule The Multiplication Rule" |
| Joint probability | Where P(A and B) when A and B are not mutually exclusive. |
| Marginal probability | Is just adding across the rows and down the columns. |
| Addition Rule | Is for A or B or Both A and B, basically for the union of A and B. |
| Complement Rule | P(Ac) = 1 - P(A) |
| Multiplication Rule | Used to calculate the joining probability of two events. Is Basically P(A|B) = P(AintB) / P(B) |
| Conditional probability | Conditional probability is used to determine how two events are related; that is, we can determine the probability of one event given the occurrence of another related event. |
| Two events are independent if? | "Test 1 P(A|B) = P(A) or P(B|A) = P(B) Test 2 P(A and B) = P(A) * P(B)" |
| Bayes Theorem Prior probability | Determined prior to the actual event. |
| Bayes Theorem Posterior probability | Or revised probability. Because the prior probability is revised after the event. |
| What is a Random Variable? | A random variable is a function or rule that assigns a number to each outcome of an experiment. Alternatively, the value of a random variable is a numerical event. |
| Discrete Random Variable | "one that takes on a countable number of values E.g. values on the roll of dice |
| Continuous Random Variable | "one whose values are not discrete, not countable E.g. time (30.1 minutes? 30.10000001 minutes?) Integers are Discrete, while Real Numbers are Continuous" |
| probability distribution | A probability distribution is a table, formula, or graph that describes the values of a random variable and the probability associated with these values. |
| Probability Notation upper case X | An upper-case letter will represent the name of the random variable, usually X. |
| Probability Notation lower case x | Its lower-case counterpart will represent the value of the random variable. |
| Discrete probability conditions | "1. The probability has to be between 0 and 1. 2. The sum of all probabilities must equal 1." |
| Probability Expected Value | The population mean is the weighted average of all of its values. The weights are the probabilities. This parameter is also called the expected value of X and is represented by E(X). |
| Probability Variance | The population variance is calculated similarly. It is the weighted average of the squared deviations from the mean. |
| Mutually exclusive events | Events that have no sample space outcomes in common , and, therefore, cannot occur simultaneously. |
| Binomial Random Variable | A random variable that is defined to be the total number of successes in n trials of a binomial experiment. Pass or fail. 1 or 0 |
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