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## What is the expected sum of the numbers on the dice?

The expected value of the random variable is (in some sense) its average value. You compute it by multiplying each value x of the random variable by the probability P(X=x), and then adding up the results. So the average sum of dice is: **E(X) = 2 ^{.} 1/36 + 3 ^{.} 2/36 +** ….

## How do you find the expected sum?

The expected value of the sum of several random variables is equal to the sum of their expectations, e.g., **E[X+Y] = E[X]+ E[Y]** . On the other hand, the expected value of the product of two random variables is not necessarily the product of the expected values.

## What is the probability of sum of two dice?

Probabilities for the two dice

Total | Number of combinations | Probability |
---|---|---|

10 | 3 | 8.33% |

11 | 2 | 5.56% |

12 | 1 | 2.78% |

Total | 36 |
100% |

## What is the probability of getting a sum of 7 when rolling two dice?

For each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes. Thus the sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is **6/36 = 1/6**.

## What is the expected value of a fair dice?

When you roll a fair die you have an equal chance of getting each of the six numbers 1 to 6. The expected value of your die roll, however, is **3.5**.

## Does expected value equal mean?

In cases **where the random variable X is real valued, expectation value and mean are same**. While mean does not take into account probability, expectation considers probability and it is probability-weighted.

## What is the difference between actual value and expected value?

In statistics, the actual value is the value that is obtained by observation or by measuring the available data. It is also called the observed value. The predicted value is the value of the variable predicted based on the regression analysis.