Martha writes down a random mathematical expression consisting of 3 single-digit positive integers with an addition sign "$+$" or a multiplication sign "$\times$" between each pair of adjacent digits. For example, her expression could be $4 + 3 \times 3$, with a value of 13. Each positive digit is equally likely, each arithmetic sign ("$+$" or "$\times$") is equally likely, and all choices are independent. What is the expected value (average value) of her expression?

Let's think step by step and output the final answer within \boxed{}.
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