Mathematical Expectation, Probability Distribution Game

[Yogurt]

I am currently working on a project in my stats class that requires me to make a game and I could use some help.

My game goes like this: The player spins a spinner that has 6 outcomes - all of equal probability/size. The player then rolls a six-sided dice and gets a number. Each spinner outcome is numbered 1-6. If the player's dice roll is equal to the spinner outcome they win a big prize. If the roll is over, they win nothing. If the roll is under they win a small prize. The player would want to get a high roll so if the spinner outcome is low, they still have a chance of winning something - small or big.

I need help with some calculations, though. First I need to know the game's probability distribution with all of its calculations shown. Then, I need the calculation of my game's mathematical expectation. Next, a sample of someone who plays my game 40 or more times. After that, a graphical display of my sample - histogram, boxplot, etc. And lastly, I need a calculation of my sample's average outcome.

Thank you so very much for anyone who helps out. You will have my eternal gratification. later

 

[Yogurt]

Hey

I tried to do the mathematical expectation but it was different now that I was dealing with 2 different aspects. (The spinner and the dice). The rest I tried understanding but were just different than the examples that were in my book/notes.

 

[pka]

From the design your outcome space is no different from tossing a pair of dice.
There are thirty-six of them.
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

The pairs on the diagonal are the big winners: 6.
The pairs in the lower triangle are minor winners: 15
The rest are losers: 15.
Each pair has the probability of 1/36.