Question

X1 x2 ,x2 are choosen independently find probability such that airthmetic mean of three number is equal to gemetric mean

Answer 1

Answer:

Let X1,X2X1,X2and X3X3 be chosen independently from the set {0,1,2,3,4}{0,1,2,3,4} each value being equally likely . What is the probability that the arithmetic mean of X1,X2X1,X2 and X3X3 is the same as their geometric mean .

My work :

My idea is to try AM≥GMAM≥GM inequality . By AM−GMAM−GM we get that equality holds only when X1=X2=X3X1=X2=X3 . So There are only 55 tuples such that X1=X2=X3X1=X2=X3 .

So required probability :

553=125

Hope it helps you.....