Question 1. A popular online war game uses probability distributions to assign damage to players injured by enemy fire. Players can be wounded by rifles, hand grenades, and dozens of other weapons until their health points drop below zero, which then the game is over for the player. The game designers model damage from a rifle with uniform distribution with R ~ uniform (2,6), and damage from a hand grenade also using a uniform distribution with H ~ uniform (1, 11).

a) When a player with only 5 health points left gets hit by each of these weapons, what is his/her chance of survival? b) What is the mean and variance of the damage from a rifle?