Editing 1374: Urn
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==Explanation== | ==Explanation== | ||
| − | A common tool for explaining concepts in elementary probability theory are games involving the drawing of coloured balls from a container, such as a bag, or hat. In older statistics related texts, a convention developed of describing the container as an urn. This is so common that such problems are often called | + | A common tool for explaining concepts in elementary probability theory are games involving the drawing of coloured balls from a container, such as a bag, or hat. In older statistics related texts, a convention developed of describing the container as an urn. This is so common that such problems are often called [[wikipedia:Urn problem|urn problems]]. |
While an {{w|urn}} can have many uses, in modern times the most common context in which it is used is to contain the burned remains of deceased individuals after a {{w|cremation}}. This is likely because as interior decor has grown more minimalist, other types of urn became less common and the association of the word urn with cremation has become ubiquitous in the vernacular. | While an {{w|urn}} can have many uses, in modern times the most common context in which it is used is to contain the burned remains of deceased individuals after a {{w|cremation}}. This is likely because as interior decor has grown more minimalist, other types of urn became less common and the association of the word urn with cremation has become ubiquitous in the vernacular. | ||
| − | [[Megan]], when asked to imagine drawing balls from an urn, imagines a cremation urn containing not only balls, but also human remains. She may be referring to a real grandfather who has been cremated, or is simply improvising a joke at Cueball's expense. | + | [[Megan]], when asked to imagine drawing balls from an urn, imagines a cremation urn containing not only balls, but also human remains. She may be referring to a real grandfather who has been cremated, or is simply improvising a joke at Cueball's expense. |
| − | The title text refers to two distinct scenarios in the | + | The title text refers to two distinct scenarios in the coloured ball experiment: The balls may be replaced between each drawing, or not. In the former case, each draw is independent of the previous, in the latter the chances of picking a particular (remaining) ball the next time have increased. Megan (or rather [[Randall]] if it is he who speaks in the title text) would prefer to put the ashes back into the urn. She might also want to have her grandfather back, and be playing with the word "replacement". |
| − | The distinction between repeated drawing with and without replacement is used in most presentations of elementary probability because it illustrates a subtle but important theoretical distinction: if the balls are replaced, one at a time, before drawing the next, the number of balls of a certain | + | The distinction between repeated drawing with and without replacement is used in most presentations of elementary probability because it illustrates a subtle but important theoretical distinction: if the balls are replaced, one at a time, before drawing the next, the number of balls of a certain colour has the {{w|binomial distribution}}, but if the balls are not replaced, so that the same ball cannot be drawn twice, you instead get the {{w|hypergeometric distribution}}. |
| − | + | In the context of this comic, drawing with replacement would mean that the dead Grandfather's ashes have been magically replaced as soon as Megan removed them from the urn. Thus, her grandfather's ashes would still remain intact & sacrosanct inside the urn. Hence the commentary pleading for it to be "drawing with replacement." Of course, such an event actually happening in real life is nonsensical, further illustrating the contrived nature of many academic problems. | |
==Transcript== | ==Transcript== | ||
