Identifying the difference between binomial and geometric random variables is important. The main difference between them is that binomial random variables have fixed trials but geometric random variables do not.
A ⭕️geometric setting arises when we perform independent trials of the same chance process and record the number of trials it takes to get one success. On each trial, the probability p of success must be the same. The number of trials Y that it takes to get one success in a geometric setting is a geometric random variable. The probability distribution of Y is a geometric distribution with probability p of success on any trial. The possible values of Y are 1, 2, 3, … n.
If Y has the geometric distribution with probability p of success on each trial, then the possible values of Y are 1, 2, 3, … if k is one of these values then you can use the Geometric probability formula: P(Y=k) = (1-p)^k-1 (p) . You can use geometricCDF or geometricPDF to calculate probabilities.
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Shape, Center, and Variability
To find the mean and standard deviation of a geometric distribution, use the following formulae:
Mean Y= 1/p ,where p is the probability of success.
Standard Deviation Y= Sqrt((1-p)/p), where p is the probability of success.
Every geometric distribution has a skewed right graph.