Two draws with replacement paying five times face

Question

A deck has $35$ cards numbered $1$ to $35$ . You draw a card, note it, return it, and draw again. Each draw pays $5$ times the number on the card. What is your expected total payout?

Short answer

$180$ . Each draw has mean value $\tfrac{1+35}{2}=18$ , so by linearity the payout averages $5\cdot18+5\cdot18=180$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Expectation, Mean, and Variance
Conditional Expectation and Variance Revisited
Continuous Random Variables and Probability Density Functions

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