In the video game, Treasure Hunter 2, each player starts with a Luck score of 0. Each time the player finds a ruby and equips it into their hat, their Luck score goes up by a random amount whose distribution is exponentially distributed with mean 1. Multiple rubies affect the Luck score independently. Once you've equipped at least one ruby, you may enter the Labyrinth in search of treasure. You are about to enter the Labyrinth with your rival, PJamma, who has 10 rubies equipped on her hat. Inside the Labyrinth, you will each find a random number of treasure chests. The underlying code of the game is such that the number of chests a player finds has a Poisson distribution with a parameter equal to that player's Luck score. After going through the Labyrinth, you see that PJamma found four treasure chests. Given this, what is the conditional density of PJamma's Luck score? Be sure to write a complete piecewise definition of this conditional density, indicating, if necessary, where it is O and where it is undefined. You may use the fact that Sor"e-i dr = n!N-n-1 for every integer n. > 0 and every nonnegative In the video game, Treasure Hunter 2, each player starts with a Luck score of 0. Each time the player finds a ruby and equips it into their hat, their Luck score goes up by a random amount whose distribution is exponentially distributed with mean 1. Multiple rubies affect the Luck score independently. Once you've equipped at least one ruby, you may enter the Labyrinth in search of treasure. You are about to enter the Labyrinth with your rival, PJamma, who has 10 rubies equipped on her hat. Inside the Labyrinth, you will each find a random number of treasure chests. The underlying code of the game is such that the number of chests a player finds has a Poisson distribution with a parameter equal to that player's Luck score. After going through the Labyrinth, you see that PJamma found four treasure chests. Given this, what is the conditional density of PJamma's Luck score? Be sure to write a complete piecewise definition of this conditional density, indicating, if necessary, where it is O and where it is undefined. You may use the fact that Sor"e-i dr = n!N-n-1 for every integer n. > 0 and every nonnegative