# Mean of Probability Distribution Calculator

**Created By :** Vaibhavi Kumari

**Reviewed By :** Rajashekhar Valipishetty

**Last Updated :** Mar 24, 2023

Simple step-by-step calculator to find the mean of the discrete probability distribution is here. This handy Mean of probability distribution calculator takes the x values, p(x) values as inputs and gives output within split seconds with detailed explanation.

### How to Find the Mean of Probability Distribution ?

To calculate the mean of any probability distribution, we have to use the following formula:

The formula for Mean or Expected Value of a probability distribution is as follows:

μ = Σx * P(x)

Where,

- x = Data value
- P(x) = Probability of value

The following are the simple steps to find the expected value or mean for the discrete probability distribution manually with ease.

- Firstly, observe the x values given in the problem and then the probability values for each random variable occured.
- Multiply the random value with its probability
- Finally, add up all the product values and get the mean of the probability distribution.

### Binomial Distribution Mean Calculator Solved Example

**Example:**

Let's consider the probability distribution for the snookers team:

X | P(X) |

2 | 0.1 |

5 | 0.2 |

6 | 0.3 |

8 | 0.4 |

**Solution:**

First, we have to multiply the corresponding X results with the related probabilities to compute the population mean μ:

X | p(X) | X * p(X) |

2 | 0.1 | 2*0.1=0.2 |

5 | 0.2 | 5 *0.2=1 |

6 | 0.3 | 6*0.3=1.8 |

8 | 0.4 | 8 * 0.4 = 3.2 |

Hence the mean of the probability distribution is calculated as:

μ = ∑ Xi * P(Xi)

= 2⋅0.1+5⋅0.2+6⋅0.3+8⋅0.4

= 6.2

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### FAQs on Handy Mean of a Binomial Probability Distribution Calculator

**1. What does P(X=x) mean?**

P(X=x) means the probability that the random variable X is equal to a specific value, indicated by x. For instance, P(X=1) refers to the probability that the random variable X is equal to 1.

**2. How do you find the mean of a probability distribution?**

https://www.youtube.com/watch?v=TXLL73ZcK1E

**3. How do you find the probability distribution on a calculator?**

https://www.youtube.com/watch?v=semdQgVYfU8

**4. What is meant by Mean of probability distribution?**

The mean in probability is a measure of central tendency of a probability distribution. It is also named as an expected value. The distribution of expected value is defined by taking various set of random samples and calculating the mean from each sample.