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Bernoulli and Binomial Distributions, Binomial Probability - Coggle Diagram
Bernoulli and Binomial Distributions
Bernoulli Trial
A single event that has only two possible outcomes
Success
Failure
Bernoulli Distribution
Probability of X
1 = Success
0 = Failure Outcome
Finding out chance of winning/
money value * Expected Value
Give us overall expected result
Probability Table
Expected Value of X =
P
Find out probability of what the question is asking
Variance of X =
Expected value
x * p(x) + (repeat)
Substitute probability value
Win value^2 * Var(X)9
Square Root of Variance Value
Binomial Distribution
Definition
Formed when a Bernoulli trial is repeated n time
If
X
Binomial (n, p)
Then
Probability of X
Solving Question
Make Probability Distribution Table for X
Find X
Substitute n with number of x-values
Sub p with probability
Substitute values into final formula to solve for P(x) in table
Binomial Probability
Probability of 'r' successes in 'n' trials of a binomial experiement
There are (n+1) possible outcomes
The probability of each outcome is given by the term in teh expansion of (q+p)^n
P
probability of success
q
probability of failure
P ( X = r)
Conditions
Only two outcomes
p & q constant for all trials
Experiments
Bernoulli
Only 1 trial
Binomial
Independent
