Definitions [4]
Definition: Probablity
Probability measures the degree of certainty of the occurrence of an event.
Definition: Continuous Random Variable
If the range of ( X ) is an interval (a, b), then ( X ) is called a continuous random variable.
Definition: Random Variable
Let ( S ) be the sample space associated with a given random experiment. Then, a real-valued function ( X ) which assigns an outcome \[w\in S\] to a unique real number X(w) is called a random variable.
Definition: Discrete Random Variable
If the range of the real function \[X:U\to R\]is a finite set or an infinite set of real numbers, then X is called a discrete random variable.
Key Points
Key Points: Concept of Probability
| No. | Term | Definition |
|---|---|---|
| 1 | Probability | A measure of the chance of occurrence of an event. |
| 2 | Random Experiment | An experiment in which all possible outcomes are known, but the exact outcome cannot be predicted with certainty. |
| 3 | Outcome | The result of a random experiment. |
| 4 | Sample Space (S) | The set of all possible outcomes of a random experiment. |
| 5 | Sample Point | Each element of the sample space. |
| 6 | Number of Sample Points | The number of elements in the sample space is denoted by n(S). |
| 7 | Equally Likely Outcomes | Outcomes which have the same chance of occurring. |
Key Points : Standard Sample Space
| No. | Term | Definition |
|---|---|---|
| 1 | Probability | A measure of the chance of occurrence of an event. |
| 2 | Random Experiment | An experiment in which all possible outcomes are known, but the exact outcome cannot be predicted with certainty. |
| 3 | Outcome | The result of a random experiment. |
| 4 | Sample Space (S) | The set of all possible outcomes of a random experiment. |
| 5 | Sample Point | Each element of the sample space. |
| 6 | Number of Sample Points | The number of elements in the sample space is denoted by n(S). |
| 7 | Equally Likely Outcomes | Outcomes which have the same chance of occurring. |
Playing Cards – Key Facts
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Total cards = 52
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Red cards = 26 (Hearts, Diamonds)
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Black cards = 26 (Clubs, Spades)
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Each suit has 13 cards
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Face cards = King, Queen, Jack (Total = 12)
