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:

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.