Make use of the Probability Distribution Calculator to find the mean, variance, standard deviation of the given data easily. Simply enter random variable value and probability and hit the calculate button to avail the mean, variance and standard deviation for the distribution in the blink of an eye with a detailed explanation.

**Probability Distribution Calculator: **Using this Probability Distribution Parameters Calculator, you can get the mean, standard deviation and variance of a distribution. In addition to the quick result, our tool also produces the step by step explanation and formulas used to calculate the probability distribution. Observe the further sections to know what is a probability distribution, what are the formulas to compute distribution parameters and how to solve probability distribution problems.

The probability distribution is defined as the possible outcomes for any random event. It is based on the underlying sample space as a set of possible outcomes for any random experiment. And the probability is the measure of uncertainty of phenomena. The random experiment is the result of an experiment, where the outcome can't be predicted.

The two types of probability distribution are listed here.

- Normal or Cumulative Probability Distribution
- Binomial or Discrete Probability Distribution

The formulas to find the mean, variance and standard deviation for a distribution are along the lines:

**Mean μ = ∑x · p(x)****Variance σ² = ∑x² · p(x) - μ²****Standard Deviation σ = √[∑x² · p(x) - μ²]**

Where,

x is the random variable number

p(x) is the probability of the experiment.

Following are the simple steps to calculate the probability distribution mean, variance, and standard deviation.

- Get the number and its probability.
- Make the values in the form of a table to read the data easily.
- Multiply the each value with its probability.
- The sum of resultant products is the mean.
- The sum of each value squared times the probability of the value occurring, minus the mean squared is variance.
- The square root of the variance is the standard deviation.

**Example:**

Find the mean, standard deviation and variance of the probability distribution?

x | p(x) |
---|---|

1 | 0.2 |

2 | 0.1 |

3 | 0.3 |

4 | 0.05 |

5 | 0.3 |

6 | 0.05 |

Solution:

The formula to calculate mean is μ = ∑x · p(x)

= 1(0.2) + 2(0.1) + 3(0.3) + 4(0.05) + 5(0.3) + 6(0.05)

= 0.2 + 0.2 + 0.9 + 0.2 + 1.5 + 0.3

= 3.3

The formul ato find variance of probability distribution is σ² = ∑x² · p(x) - μ²

∑x² · p(x) = (1² . 0.2) + (2² . 0.1) + (3² . 0.3) + (4² . 0.05) + (5² . 0.3) + (6² . 0.0.5)

= 0.2 + 0.4 + 2.7 + 0.8 + 7.5 + 1.8

= 13.4

σ² = 13.4 - 3.3²

= 2.51

Standard deviation σ = √2.51

= 1.584

Check Probabilitycalculatorguru to find the parameters of probability distribution of any data easily & quickly.

** 1. What does mean by probability? **

Probability is defined as the occurrence of an event. It is the ratio of the number of favorable outcomes to the total number of outcomes in an event.

**2. How do you calculate probability distribution?**

Give each value and its probability in the mentioned input boxes of the calculator and press the calculate button to find the probability distribution mean, standard deviation and variance easily.

**3. What are the rules for probability distributions?**

The two conditions of the probability for a discrete random variable is function f(x) must be nonnegative for each value of the random variable and second is the sum of probabilities for each value of the random variable must be equal to 1.

**4. What are the steps in constructing a probability distribution?**

- At first, write the number of widgets in one line.
- Beside each value, write its probability.
- Make a note that, the sum of probabilities should be equal to 1.