If you eat $10$ pigs in $40\%$ of the weeks, $7$ pigs in $27\%$ of the weeks and $5$ pigs in $33\%$ of the weeks while cooking $10$ pigs at the beginning of the week to have sufficient supply (the uneaten pigs are thrown out), what is the probability distribution of the weekly consumption of pigs?
Would it be $0.4 \cdot 10+ 0.27 \cdot 7+ 0.33 \cdot 5$? Thank you.