10 bernoulli trials with a success probability of 0.45

Publish date: 2024-05-16
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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
1Success0.4510.55(1 - 1)0.45 x 10.45
2Failure0.4500.55(1 - 0)1 x 0.550.55
3Success0.4510.55(1 - 1)0.45 x 10.45
4Failure0.4500.55(1 - 0)1 x 0.550.55
5Failure0.4500.55(1 - 0)1 x 0.550.55
6Failure0.4500.55(1 - 0)1 x 0.550.55
7Failure0.4500.55(1 - 0)1 x 0.550.55
8Success0.4510.55(1 - 1)0.45 x 10.45
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:

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

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What is the Answer?

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 trialsRepeating an experiment using a bernoulli distributionexpected valuepredicted value of a variable or event
E(X) = ΣxI · P(x)kurtosisstatistical measure describing the distribution, or skewness, of observed data around the mean. Also referred to as the volatility of volatilitymeanA statistical measurement also known as the averagemedianthe value separating the higher half from the lower half of a data sample,probabilitythe 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 Outcomesskewness measure of the asymmetry of the probability distribution of a real-valued random variable about its meantriala single performance of well-defined experimentvarianceHow 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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