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 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 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 | Failure | 0.7500.25(1 - 0) | 1 x 0.25 | 0.25 |
| 10 | Failure | 0.7500.25(1 - 0) | 1 x 0.25 | 0.25 |
| 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 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 14 | Failure | 0.7500.25(1 - 0) | 1 x 0.25 | 0.25 |
| 15 | Failure | 0.7500.25(1 - 0) | 1 x 0.25 | 0.25 |
| 16 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 17 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
| 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 | Success | 0.7510.25(1 - 1) | 0.75 x 1 | 0.75 |
Compare Expected to Actual Results:
Given your success probability of 0.75:
we expect 0.75 x 20 = 15 successes
Our actual results were 15 successes and 5 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 = 0.75
Median = 1
Variance = 0.1875
Skewness = -1.1547005383793
Kurtosis = -0.66666666666667
Entropy = -0.034238445661164
You have 1 free calculations remaining
What is the Answer?
Probability = 0.75
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.
What 3 formulas are used for the Bernoulli Trials Calculator?
pkqn - kp = success probability
q = 1 - p
For more math formulas, check out our Formula Dossier
What 9 concepts are covered in the Bernoulli Trials Calculator?
bernoulli trialsRepeating an experiment using a bernoulli distributionexpected valuepredicted value of a variable or eventE(X) = ΣxI · P(x)kurtosisstatistical measure describing the distribution, or skewness, of observed data around the mean. Also referred to as the volatility of volatilitymeanA statistical measurement also known as the averagemedianthe value separating the higher half from the lower half of a data sample,probabilitythe 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 Outcomesskewness measure of the asymmetry of the probability distribution of a real-valued random variable about its meantriala single performance of well-defined experimentvarianceHow 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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