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# Probability distributions calculator

This calculator finds mean, standard deviation and variance of a distribution. The calculator will generate a step by step explanation along with the graphic representation of the data sets and regression line.

Probability Distributions Calculator
mean, standard deviation and variance of a distribution
help ↓↓ examples ↓↓
All possible outcomes are equally likely
Use data grit to input $X$ and $P(x)$
 Find the Mean (expectation) of a distribution Find the Standard Deviation of a distribution Find the Variance of a distribution
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Examples
ex 1:

A company tested a new product and found that the number of errors per 100 products had the following probability distribution:

$$\begin{array}{c|ccccc} number~of~errors (X) & ~2~ & ~3~ & ~4~ & ~5~ & ~6 \\ P(X) & ~0.02~ & ~0.25~ & ~0.4~ & ~0.3~ & ~0.03 \end{array}$$

Find the mean number of errors per 100 products.

ex 2:

You flip the coin. What is the expected value if every time you get heads, you lose \$2, and every time you get tails, you gain \$5. The probability distribution is:

$$\begin{array}{c|ccccc} \text{money gain} & -2 & 5 \\ P(X) & 0.5 & 0.5 \end{array}$$
ex 3:

The discrete probability distribution of X is given by:

$$\begin{array}{c|ccccc} X & ~0~ & ~2~ & ~5~ & ~7/3~ & ~5 \\ P(X) & ~0.1~ & ~0.2~ & ~1/3~ & ~1/6~ & ~0.2 \end{array}$$

Find the mean of the distribution.

ex 4:

When you roll a die, you will be paid \$3 for numbers divisible by 3 and you will lose \$2 for numbers that are not divisible by 3 Find the expected value of money you get.

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