Information AboutMemorylessness |
| CATEGORIES ABOUT MEMORYLESSNESS | |
| probability theory | |
|
''For the use of the term in Materials Science see Hysteresis .'' For example, suppose a die is thrown as many times as it takes to get a "1", so that the probability of "success" on each trial is 1/6, and the random variable ''X'' is the number of times the die must be thrown. Then ''X'' has a geometric distribution, and the Conditional Probability that the die must be thrown at least four more times to get a "1", given that it has already been thrown 10 times without a "1" appearing, is no different from the original probability that the die would be thrown at least four times. In effect, the random process does not "remember" how many failures have occurred so far. DISCRETE MEMORYLESSNESS Suppose ''X'' is a Discrete Random Variable whose values lie in the set { 0, 1, 2, ... } or in the set { 1, 2, 3, ... }. The probability distribution of ''X'' is memoryless precisely if for any ''x'', ''y'' in { 0, 1, 2, ... } or in { 1, 2, 3, ... }, (as the case may be), we have : | ||
| Memorylessness Is Often Misunderstood By Students Taking Courses On Probability: The Fact That Pr(''X'' > 13 ''X'' > 10) | Pr(''X'' > 3) does ''not'' mean that the events ''X'' > 13 and ''X'' > 10 are Independent ie, it does ''not'' mean that Pr(''X'' > 13 ''X'' > 10) = Pr(''X'' > 13) To summarize: "memorylessness" of the probability distribution of the number of trials ''X'' until the first success means |
|
| :<math>\Pr(X > T + S X > T) | \Pr(X > s)\,</math> |
|
|