Find a formula for p(x) = P(X=x)

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The discussion focuses on deriving the probability mass function p(x) = P(X=x) for a discrete random variable X that takes on two values, a and b. The probabilities are defined as P(X=a) = p and P(X=b) = 1-p. The expected value, denoted as mu = E(X), can be expressed as E(X) = a*p + b*(1-p), establishing a direct relationship between the probabilities and the expected value.

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Find a formula for p(x) = P(X=x) ...

So I have a test tomorrow and this question is in a list of review questions and I'm having trouble remembering where the mu fits into the formula. Any help would be greatly appreciated :)

Question: Suppose that X is a random variable with just two possible values a and b. For x = a and b find a formula for p(x) = P(X = x) in terms of a, b and mu = E(X).
 
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If P(X=a)=p and P(X=b)=1-p, what can you say about E(X)?
 

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