Chapter 8.1, Problem 2E

Dungeons and Dragons: Part A A 20-sided die is often used in tabletop role-playing games like Dungeons and Dragons.  During the game players may face something called a "skill check" where they must roll a 20-sided die and get a result equal to or above a given value.  For example, a player may be required to roll a 15 or above in order to succeed and pass the skill check.  Rolling a 14 or lower would be a failure.  If the player rolls the die 10 times in a row, what is the expected number of rolls that would pass the skill check by rolling as a 15 or higher? For the previous calculations, what is the standard deviation for the number of times the die would be rolled 15 or above During a game of Dungeons and Dragons, the previously-mentioned player rolls the 20-sided die 30 times in total.  What is the probablity that they successfully roll a 15 or higher exactly 7 times during that game? Express your final answer as a percentage to 2 decimal places.

f E and F are disjoint events, P(E and F) =

Find the cdf of a random variable Y whose pdf is given by; 2, 0≤x≤1 1/3, 0≤x≤1 a) f(x)=3, 2≤x≤4 0, elsewhere 2, 1≤x≤2 b) f(x)= (3-x)2, 2≤x≤3 0, elsewhere