# 10 bernoulli trials with a success probability of 0.45

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

Simulate 10 bernoulli trials with a success probability of 0.45.
The Bernoulli Trial formula is pkqn - k where p = success probability, q = 1 - p

Trial #Success/FailureMath WorkMath Work IIProbability
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
5Failure0.4500.55(1 - 0)1 x 0.550.55
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 would have expected 0.45 x 10 = 4.5 successes
Our actual results were 2 successes and 8 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, 0.55 > 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 0.31

Skewness = 0.84

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 = -

Entropy = -qLn(q) - pLn(p)
Entropy = -(0.55)Ln(0.55) - 0.45Ln(0.45)
Entropy = -(0.55)(-0.62) - 0.45(-0.77)
Entropy = -(-0.59) - -0.
Entropy = -0.