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- Probability Distributions Calculator
Probability distributions calculator
Enter a probability distribution table and this calculator will find the mean, standard deviation and variance. The calculator will generate a step by step explanation along with the graphic representation of the data sets and regression line.
solution
You entered the following data:
$$\begin{array}{c|ccccc}X&5000&2000&1000&500&0\\P(X)&0.0228&0.0338&0.0654&0.459&0.419\end{array}$$The standard deviation of the given distribution is:
$$ \sigma = 811.3555 $$explanation
In order to find the standard deviation of the given distribution, we will use the following formula:
$$ \sigma = \sqrt{\sum{x^2 \cdot p(x) } - \mu^2}$$
In this example:
$$ \mu = 476.5 $$(use "Find the Mean" option in this calculator for the step-by-step explanation on how to find mean)
Now we will find the sum:
$$ \begin{aligned}\sum{x^2 \cdot p(x) } &= 5000^2\cdot0.0228+2000^2\cdot0.0338+1000^2\cdot0.0654+500^2\cdot0.459+0^2\cdot0.419 \\\sum{x^2 \cdot p(x) } &= 885350\end{aligned}$$Putting all together we have:
$$ \sigma = \sqrt{\sum{x^2 \cdot p(x) } - \mu^2} = \sqrt{ 885350 - 476.5^2 } = \sqrt{ 658298 } \approx 811.3555$$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.
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:
$$ \begin{array}{c|ccccc} \text{money gain} & -2 & 5 \\ P(X) & 0.5 & 0.5 \end{array} $$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.
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.
Please tell me how can I make this better.