The difference between Arbitrary and Random
When used as nouns, arbitrary means anything arbitrary, such as an arithmetical value or a fee, whereas random means a roving motion.
When used as adjectives, arbitrary means based on individual discretion or judgment, whereas random means having unpredictable outcomes and, in the ideal case, all outcomes equally probable.
check bellow for the other definitions of Arbitrary and Random
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Arbitrary as an adjective (usually, of a decision):
Based on individual discretion or judgment; not based on any objective distinction, perhaps even made at random.
Examples:
"Benjamin Franklin's designation of "positive" and "negative" to different charges was arbitrary."
"The decision to use 18 years as the legal age of adulthood was arbitrary, as both age 17 and 19 were reasonable alternatives."
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Arbitrary as an adjective:
Determined by impulse rather than reason; heavy-handed.
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Arbitrary as an adjective (mathematics):
Any, out of all that are possible.
Examples:
"The equation is true for an arbitrary value of x."
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Arbitrary as an adjective:
Determined by independent arbiter.
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Arbitrary as an adjective (linguistics):
Not representative or symbolic; not iconic.
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Arbitrary as a noun:
Anything arbitrary, such as an arithmetical value or a fee.
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Random as a noun:
A roving motion; course without definite direction; lack of rule or method; chance.
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Random as a noun (obsolete):
Speed, full speed; impetuosity, force.
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Random as a noun (obsolete):
The full range of a bullet or other projectile; hence, the angle at which a weapon is tilted to allow the greatest range.
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Random as a noun (figuratively, colloquial):
An undefined, unknown or unimportant person; a person of no consequence.
Examples:
"The party was boring. It was full of randoms."
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Random as a noun (mining):
The direction of a rake-vein.
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Random as an adjective:
Having unpredictable outcomes and, in the ideal case, all outcomes equally probable; resulting from such selection; lacking statistical correlation.
Examples:
"The flip of a fair coin is purely random."
"The newspaper conducted a random sample of five hundred American teenagers."
"The results of the field survey look random by several different measures."
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Random as an adjective (mathematics):
Of or relating to probability distribution.
Examples:
"A toss of loaded dice is still random, though biased."
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Random as an adjective (computing):
Pseudorandom; mimicking the result of random selection.
Examples:
"The <tt>rand</tt> function generates a random number from a seed."
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Random as an adjective (somewhat colloquial):
Representative and undistinguished; typical and average; selected for no particular reason.
Examples:
"A random American off the street couldn't tell the difference."
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Random as an adjective (somewhat colloquial):
Apropos of nothing; lacking context; unexpected; having apparent lack of plan, cause or reason.
Examples:
"That was a completely random comment."
"The teacher's bartending story was interesting, but random."
"The narrative takes a random course."
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Random as an adjective (colloquial):
Characterized by or often saying random things; habitually using non sequiturs.
Examples:
"You're so random!"