# 20 bernoulli trials with a success probability of 0.75

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

Simulate 20 bernoulli trials with a success probability of 0.75.
The Bernoulli Trial formula is pkqn - k where p = success probability, q = 1 - p

Trial #Success/FailureMath WorkMath Work IIProbability
1Failure0.7500.25(1 - 0)1 x 0.250.25
2Success0.7510.25(1 - 1)0.75 x 10.75
3Success0.7510.25(1 - 1)0.75 x 10.75
4Failure0.7500.25(1 - 0)1 x 0.250.25
5Success0.7510.25(1 - 1)0.75 x 10.75
6Success0.7510.25(1 - 1)0.75 x 10.75
7Success0.7510.25(1 - 1)0.75 x 10.75
8Success0.7510.25(1 - 1)0.75 x 10.75
9Success0.7510.25(1 - 1)0.75 x 10.75
10Success0.7510.25(1 - 1)0.75 x 10.75
11Success0.7510.25(1 - 1)0.75 x 10.75
12Failure0.7500.25(1 - 0)1 x 0.250.25
13Failure0.7500.25(1 - 0)1 x 0.250.25
14Success0.7510.25(1 - 1)0.75 x 10.75
15Success0.7510.25(1 - 1)0.75 x 10.75
16Failure0.7500.25(1 - 0)1 x 0.250.25
17Success0.7510.25(1 - 1)0.75 x 10.75
18Success0.7510.25(1 - 1)0.75 x 10.75
19Failure0.7500.25(1 - 0)1 x 0.250.25
20Success0.7510.25(1 - 1)0.75 x 10.75

Compare Expected to Actual Results:
Given your success probability of 0.75, we would have expected 0.75 x 20 = 15 successes
Our actual results were 14 successes and 6 failures

Calculate the median:
The median of the bernoulli trial works as follows:
• 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 0.22

Skewness = -3

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 = -0.67

Entropy = -qLn(q) - pLn(p)
Entropy = -(0.25)Ln(0.25) - 0.75Ln(0.75)
Entropy = -(0.25)(-9) - 0.75(-0.78)
Entropy = -(-0.97) - -0.84
Entropy = -0.164