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To elaborate on @jtbell #24. The expectation value, as you know, is an average.
Suppose you performed ##N## measurements of the momentum at random intervals and you got ##N_1## values at ##+p## and ##N_2## at ##-p##, where ##N=N_1+N_2##. What is the average value of the momentum?
Suppose you flip a fair coin ##N## times and you get ##N_1## tails and ##N_2## heads. You assign +1 point to tails and -1 point to heads. How would you express the average of the flips as a number? What do you think the a priori average could be before you do any measurements?
Suppose you performed ##N## measurements of the momentum at random intervals and you got ##N_1## values at ##+p## and ##N_2## at ##-p##, where ##N=N_1+N_2##. What is the average value of the momentum?
Suppose you flip a fair coin ##N## times and you get ##N_1## tails and ##N_2## heads. You assign +1 point to tails and -1 point to heads. How would you express the average of the flips as a number? What do you think the a priori average could be before you do any measurements?