6. ExpectiMax Your little brother Timmy has a birthday and he was promised a toy. However, Timmy has been misbehaving lately and Dad thinks he deserves the least expensive present. Timmy, of course, wants the most expensive toy. Dad will pick the city from which to buy the toy, Timy l pick the store and you get to pick the toy itself. You don't want to take sides so you decide to pick a toy at random All prices (ineluding X and Y) are assumed to be nonnegative. Dad Emeryville Berkeley Little Timmy Games of Berkeley Five Little Monkeys The Ark oys RUs You 50 $20 $50 $30 $25 S35 X $36 Y (a) 1 pt Fill in the values of all the nodes that don't depend on X or Y (b) [3 pts What values of X will make Dad pick Emeryville regardless of the price of Y? (c) 3 pts] We know that Y is at most $30. What values of X will result in a toy from Games of Berkeley regardless of the exact price of Y? (d) [2 pts] Normally, alpha-beta pruning is not used with expectimax. However, with some additional information, it is possible to do something similar. Which one of the following conditions on a problem are required to perform pruning with expectimax? 1. The children of the expeetation node are leaves. 2. All values are positive. 3. The children of the expectation node have specified ranges. 4. The child to prune is last