Simulate 20 bernoulli trials with:
a success probability p = 0.75
Bernoulli Trial Formula
pkqn - k
where p = success probability, q = 1 - p
Bernoulli Trial Table
| Trial # | Success/Failure | Math Work 1 | Math Work 2 | Probability |
|---|---|---|---|---|
| 1 | Failure | 0.7500.25(1 - 0) | 1 x 0.25 | 0.25 |
| 2 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 3 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 4 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 5 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 6 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 7 | Failure | 0.7500.25(1 - 0) | 1 x 0.25 | 0.25 |
| 8 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 9 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 10 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 11 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 12 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 13 | Failure | 0.7500.25(1 - 0) | 1 x 0.25 | 0.25 |
| 14 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 15 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 16 | Failure | 0.7500.25(1 - 0) | 1 x 0.25 | 0.25 |
| 17 | Failure | 0.7500.25(1 - 0) | 1 x 0.25 | 0.25 |
| 18 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 19 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 20 | Failure | 0.7500.25(1 - 0) | 1 x 0.25 | 0.25 |
Compare Expected to Actual Results:
Given your success probability of 0.75:
we expect 0.75 x 20 = 15 successes
Our actual results were 14 successes and 6 failures
Calculate the median:
- If q > p, 0
- If q = p, 0.5
- If q < p, 1
Since q < p, 0.25 < 0.75, then our median is 1
Calculate Variance:
Variance σ2 = pq or p(1 - p)
Variance σ2 = (0.75)(0.25)
Variance σ2 = 0.1875
Calculate Skewness:
| Skewness = | q - p |
| √pq |
| Skewness = | 0.25 - 0.75 |
| √(0.75)(0.25) |
| Skewness = | -0.5 |
| √0.1875 |
| Skewness = | -0.5 |
| 0.43301270189222 |
Skewness = -1.1547005383793
Calculate Kurtosis:
| Kurtosis = | 1 - 6pq |
| √pq |
| Kurtosis = | 1 - 6(0.75)(0.25) |
| (0.75)(0.25) |
| Kurtosis = | 1 - 6(0.1875) |
| 0.1875 |
| Kurtosis = | 1 - 1.125 |
| 0.1875 |
| Kurtosis = | -0.125 |
| 0.1875 |
Kurtosis = -0.66666666666667
Calculate Entropy:
Entropy = -qLn(q) - pLn(p)
Entropy = -(0.25)Ln(0.25) - 0.75Ln(0.75)
Entropy = -(0.25)(-1.3862943611199) - 0.75(-0.28768207245178)
Entropy = -(-0.34657359027997) - -0.21576155433884
Entropy = -0.034238445661164
Answer Summary:
Probability = 0.25
Median = 1
Variance = 0.1875
Skewness = -1.1547005383793
Kurtosis = -0.66666666666667
Entropy = -0.034238445661164
Median = 1
Variance = 0.1875
Skewness = -1.1547005383793
Kurtosis = -0.66666666666667
Entropy = -0.034238445661164
You have 2 free calculationss remaining
What is the Answer?
Probability = 0.25
Median = 1
Variance = 0.1875
Skewness = -1.1547005383793
Kurtosis = -0.66666666666667
Entropy = -0.034238445661164
Median = 1
Variance = 0.1875
Skewness = -1.1547005383793
Kurtosis = -0.66666666666667
Entropy = -0.034238445661164
How does the Bernoulli Trials Calculator work?
Free Bernoulli Trials Calculator - Given a success probability p and a number of trials (n), this will simulate Bernoulli Trials and offer analysis using the Bernoulli Distribution. Also calculates the skewness, kurtosis, and entropy
This calculator has 2 inputs.
This calculator has 2 inputs.
What 3 formulas are used for the Bernoulli Trials Calculator?
What 9 concepts are covered in the Bernoulli Trials Calculator?
- bernoulli trials
- Repeating an experiment using a bernoulli distribution
- expected value
- predicted value of a variable or event
E(X) = ΣxI · P(x) - kurtosis
- statistical measure describing the distribution, or skewness, of observed data around the mean. Also referred to as the volatility of volatility
- mean
- A statistical measurement also known as the average
- median
- the value separating the higher half from the lower half of a data sample,
- probability
- the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes - skewness
- measure of the asymmetry of the probability distribution of a real-valued random variable about its mean
- trial
- a single performance of well-defined experiment
- variance
- How far a set of random numbers are spead out from the mean
Example calculations for the Bernoulli Trials Calculator
Bernoulli Trials Calculator Video
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