Question

In 2001, 112 of 519 applicants to the PhD program in economics at a prestigious university listed the U.S. as their country of citizenship The next year there are 680 applicants, 204 of whom are U.S. citizens. Can the difference be attributed to randomness alone? i.e., is the probability of a PhD applicant to be a U.S. citizen the same in 2001 and 2002?

Answer 1

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Randomness and probability are different concepts but are related. Randomness was linked to cause and effect. the areat and later randomness linked to probability but the conception of randomnes would depend on the view. so the difference can't be attributed to randomness alone example:- Take toon a coin each outcome is equally probable, if the coin is fair.&o, the corresponding probability is y, for each outcome Image if the coin is biased, then it would obuously different probability distribution Example 2: Take a dice, 6 faces. if somehow, the die is tampered, then obviously 'randomness would be biased towarda comething which makes probability distributions non-uniform. Probability of PhD applicabt in 2001 - 112 519 = 0.2158 Probability of PhD applicant in 2002 = 204/ 7680 = 0.3 Probabilities in 2001 € 2002 are different.