Reference no: EM131832982
Show that the following quantities are random variables by explaining how they may be defined as functions on a probability space:
(i) The sum of 2 dice that are tossed independently.
(ii) The number of times a coin is tossed until a head appears for the first time.
(iii) The second digit in the decimal expansion of a number chosen on the unit interval in accordance with a uniform probability law.
(iv) The absolute value of a number chosen on the real line in accordance with a normal probability law.
(v) The number of urns that contain balls bearing the same number, when 52 balis, numbered I to 52, are distributed, one to an urn, among 52 urns, numbered 1 to 52.
(vi) The distance from the origin of a 2-tuple (x1, x2) in the plane chosen in accordance with a known probability law, specified by the probability density function f(x1, x2).
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Obeys the central limit theorem
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Functions on a probability space
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