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show that the following quantities are random variables by explaining how they may be defined as functions on a
a number denoted by x1gt is chosen at random from the set of integers i 2 3 4 a second number denoted by x2 is chosen
suppose the probability is equal to p that the weather rain or no rain on any arbitrary day is the same as on the
suppose you are confronted with 2 coins a and b you are to make n tosses using the coin you prefer at each toss you
suppose that people in a certain group may be classified into 2 categories say city dwellers and country dwellers
random walk with retaining barriers consider a straight line on which positions 0 1 2 7 are marked off consider a man
consider 2 urns i and ii each of which contains 1 white and 1 red ball one ball is drawn simultaneously from each urn
from an urn containing 6 white and 4 black balls 5 balls are transferred into an empty second urn from it 3 balls are
consider an urn containing 12 balls of which 8 are white let a sample of size 4 be drawn with replacement without
consider a box containing 5 radio tubes selected at random from the output of a machine which is known to be 20
in a certain college the geographical distribution of men students is as follows 50 come from the east 30 come from the
consider an urn containing 10 balls of which 4 are white choose an integer nat random from the set i 2 3 4 s 6 and then
each of 3 boxes identical in appearance has 2 drawers box a contains a gold coin in each drawer box b contains a silver
three prisoners whom we may call a b and c are informed by their jailer that one of them has been chosen at random to
a male rat is either doubly dominant aa or heterozygous aa owing to mendelian properties the probabilities of either
consider a sample of size 3 drawn in the following manner one starts with an urn containing 5 white and 7 red balls at
let the probability that a person aged x years will survive i year be denoted by px whereas qxnbsp 1 - pxnbspis the
consider a young man who is waiting for a young lady who is late to amuse himself while waiting he decides to take a
do the preceding exercise under the assumption that the coin tossed by the young man is unfair and has probability 051
let 4 persons play the game of odd man out with fair coins what is the probability for n 1 2 that n plays will be
a man wants to open his door he has 5 keys only i of which fits the door he tries the keys successively choosing them i
a man makes 5 independent throws of a dart at a target let p denote his probability of hitting the target at each throw
consider a loaded die in 10 independent throws the probability that an even number will appear 5 times is twice the
an accident insurance company finds that 0001 of the population incurs a certain kind of accident each year assuming
a certain airline finds that 4 per cent of the persons making reservations on a certain flight will not show up for the