Question

In: Statistics and Probability

You pay $1 to play a game. The game consists of rolling a pair of dice....

You pay $1 to play a game. The game consists of rolling a pair of dice. If you observe a sum of 7 or 11 you receive $4. If not, you receive nothing. Compute the expected value and standard deviation for this game?

Solutions

Expert Solution

Hello Sir/ Mam

YOUR REQUIRED ANSWERS ARE

Expected Value -0.11
S.D. 2.2879

Given that:

Payment to play the game = $1

If sum 7 or 11, then = $4

Otherwise, = $0

We know that:

x 2 3 4 5 6 7 8 9 10 11 12
P(X=x) 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36
Dice Outcome Earnings Probability
7 or 11 3 0.2222
Otherwise -1 0.7778

Hence,

Dice Outcome Earnings Probability E*P
7 or 11 3 0.2222 0.67
Otherwise -1 0.7778 -0.78
Expected Value -0.11
Dice Outcome Earnings Probability E*P (Earnings-Mean)^2
7 or 11 3 0.2222 0.67 9.68
Otherwise -1 0.7778 -0.78 0.79
Total -0.11 10.47

Now,

I hope this solves your doubt.

Do give a thumbs up if you find this helpful.

orchestra answered 2 years ago
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