I have an exercise where I struggle to understand a below sentence:
X (prior) is a discrete random variable that takes the value 1 with probability $ p \in \{0,1\} $ , and the -1 value with probability 1-p.
The part which confuse mi is the $ p \in \{0,1\} $. This is mean, 50% of the probability the X = 1 and 50% for X = -1? So in this case: $ P_X(x=1) = p = 1/2 $? I have just thought this because there are two elements, and the text does not give any further explanation of what is the probability of the different X values.
Or it is not sure, and we don't know the P_X(x=1)?
Regards
X is a random variable that here has two possible outcomes, 1 or -1.
p is a probability, hence can only take values in the range [0,1]
You said that P(X=1) = p, therefore as the only other possible outcome for X is -1, we must have P(X=-1) = 1-p, as the sum of the probability of all possible outcomes is 1.
Here p is unknown