In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a clear distinction in perspective: the number that is the probability of some observed outcomes given a set of parameter values is regarded as the likelihood of the set of parameter values given the observed outcomes.
Suppose you have a coin with probability p to land heads and (1-p) to land tails. Let x=1 indicate heads and x=0 indicate tails. Define f as follows
f(x,p)=p^x (1-p)^{1-x}
f(x,2/3) is probability of x given p=2/3, f(1,p) is likelihood of p given x=1. Basically likelihood vs. probability tells you which parameter of density is considered to be the variable
Suppose you have a coin with probability p to land heads and (1-p) to land tails. Let x=1 indicate heads and x=0 indicate tails. Define f as follows
f(x,p)=p^x (1-p)^{1-x}
f(x,2/3) is probability of x given p=2/3, f(1,p) is likelihood of p given x=1. Basically likelihood vs. probability tells you which parameter of density is considered to be the variable
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