Simulate 10 bernoulli trials with:
a success probability p = 0.45
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 | 0.4500.55(1 - 0) | 1 x 0.55 | 0.55 |
| 2 | Failure | 0.4500.55(1 - 0) | 1 x 0.55 | 0.55 |
| 3 | Success | 0.4510.55(1 - 1) | 0.45 x 1 | 0.45 |
| 4 | Success | 0.4510.55(1 - 1) | 0.45 x 1 | 0.45 |
| 5 | Success | 0.4510.55(1 - 1) | 0.45 x 1 | 0.45 |
| 6 | Success | 0.4510.55(1 - 1) | 0.45 x 1 | 0.45 |
| 7 | Failure | 0.4500.55(1 - 0) | 1 x 0.55 | 0.55 |
| 8 | Failure | 0.4500.55(1 - 0) | 1 x 0.55 | 0.55 |
| 9 | Failure | 0.4500.55(1 - 0) | 1 x 0.55 | 0.55 |
| 10 | Failure | 0.4500.55(1 - 0) | 1 x 0.55 | 0.55 |
Compare Expected to Actual Results:
Given your success probability of 0.45:
we expect 0.45 x 10 = 4.5 successes
Our actual results were 4 successes and 6 failures
Calculate the median:
- If q > p, 0
- If q = p, 0.5
- If q < p, 1
Since q > p, 0.55 > 0.45, then our median is 0
Calculate Variance:
Variance σ2 = pq or p(1 - p)
Variance σ2 = (0.45)(0.55)
Variance σ2 = 0.2475
Calculate Skewness:
| Skewness = | q - p |
| √pq |
| Skewness = | 0.55 - 0.45 |
| √(0.45)(0.55) |
| Skewness = | 0.1 |
| √0.2475 |
| Skewness = | 0.1 |
| 0.49749371855331 |
Skewness = 0.20100756305184
Calculate Kurtosis:
| Kurtosis = | 1 - 6pq |
| √pq |
| Kurtosis = | 1 - 6(0.45)(0.55) |
| (0.45)(0.55) |
| Kurtosis = | 1 - 6(0.2475) |
| 0.2475 |
| Kurtosis = | 1 - 1.485 |
| 0.2475 |
| Kurtosis = | -0.485 |
| 0.2475 |
Kurtosis = -1.959595959596
Calculate Entropy:
Entropy = -qLn(q) - pLn(p)
Entropy = -(0.55)Ln(0.55) - 0.45Ln(0.45)
Entropy = -(0.55)(-0.59783700075562) - 0.45(-0.79850769621777)
Entropy = -(-0.32881035041559) - -0.359328463298
Entropy = -0.190671536702
Answer Summary:
Probability = 0.55
Median = 0
Variance = 0.2475
Skewness = 0.20100756305184
Kurtosis = -1.959595959596
Entropy = -0.190671536702
Median = 0
Variance = 0.2475
Skewness = 0.20100756305184
Kurtosis = -1.959595959596
Entropy = -0.190671536702
You have 2 free calculationss remaining
What is the Answer?
Probability = 0.55
Median = 0
Variance = 0.2475
Skewness = 0.20100756305184
Kurtosis = -1.959595959596
Entropy = -0.190671536702
Median = 0
Variance = 0.2475
Skewness = 0.20100756305184
Kurtosis = -1.959595959596
Entropy = -0.190671536702
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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