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Kanya Shah

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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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*.

🎥**Watch: AP Stats - ****Probability: Random Variables, Binomial/Geometric Distributions**

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