Binomial distribution (HSC SSCE Mathematics Extension 1): Flashcards
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What does the binomial distribution model?
What does the binomial distribution model?
It models successes in independent Bernoulli trials.
Define a Bernoulli trial.
Define a Bernoulli trial.
An experiment with two outcomes: success or failure.
What is the success probability denoted as?
What is the success probability denoted as?
It is denoted as 'p' in binomial distribution.
What does 'n' represent in binomial distribution?
What does 'n' represent in binomial distribution?
'n' is the number of independent trials conducted.
What is the formula for the probability mass function?
What is the formula for the probability mass function?
P(X = x) = C(n, x) p^x (1-p)^(n-x)
What does the binomial coefficient represent?
What does the binomial coefficient represent?
It shows how to choose x successes from n trials.
How does increasing 'p' affect the distribution?
How does increasing 'p' affect the distribution?
A higher p skews the distribution to the right.
What is the mean of a binomial distribution?
What is the mean of a binomial distribution?
Mean is E(X) = np.
What is the variance of a binomial distribution?
What is the variance of a binomial distribution?
Variance is Var(X) = np(1-p).
What can invalidate the binomial model?
What can invalidate the binomial model?
Dependent trials or changing probabilities can invalidate it.