<-- Enter p
<-- Enter number of trials

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/FailureMath Work 1Math Work 2Probability
1Failure0.4500.55(1 - 0)1 x 0.550.55
2Failure0.4500.55(1 - 0)1 x 0.550.55
3Failure0.4500.55(1 - 0)1 x 0.550.55
4Success0.4510.55(1 - 1)0.45 x 10.45
5Success0.4510.55(1 - 1)0.45 x 10.45
6Success0.4510.55(1 - 1)0.45 x 10.45
7Failure0.4500.55(1 - 0)1 x 0.550.55
8Failure0.4500.55(1 - 0)1 x 0.550.55
9Failure0.4500.55(1 - 0)1 x 0.550.55
10Failure0.4500.55(1 - 0)1 x 0.550.55

##### 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 3 successes and 7 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 0.497494

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

Probability = 0.55
Median = 0
Variance = 0.2475
Skewness = 0.20100756305184
Kurtosis = -1.959595959596
Entropy = -0.190671536702

Probability = 0.55
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.

### What 3 formulas are used for the Bernoulli Trials Calculator?

pkqn - k
p = 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 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