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## How do you find the expected value of dice rolls?

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 value of the 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 expected value of the sum of two dice rolls?

The expectation of the sum of two (independent) dice is the sum of expectations of each die, which is **3.5 + 3.5 = 7**. Similarly, for N dice throws, the expectation of the sum should be N * 3.5. If you’re taking only the maximum value of the two dice throws, then your answer 4.47 is correct.

## How do you calculate expectation?

The basic expected value formula is the probability of an event multiplied by the amount of times the event happens: **(P(x) * n)**. The formula changes slightly according to what kinds of events are happening.

## How do you find the expected value?

**How to find the expected value?**

- Multiply each random value by its probability of occurring.
- Sum all the products from Step 1.
- The result is the expected value.

## What is the expected value of XY?

– The expectation of the product of X and Y is the product of the individual expectations: **E(XY ) = E(X)E(Y )**. More generally, this product formula holds for any expectation of a function X times a function of Y . For example, E(X2Y 3) = E(X2)E(Y 3).

## What is the expected value quizlet?

**The chance that some event will occur based on known characteristics or facts**.

## What is the probability of getting a sum of 8 when you roll 2 dice?

Probabilities for the two dice

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

7 | 6 | 16.67% |

8 | 5 |
13.89% |

9 | 4 | 11.11% |

10 | 3 | 8.33% |