Geometric Distribution Calculator

✖Probability of Success in Binomial Distribution is the likelihood of winning an event.ⓘ Probability of Success in Binomial Distribution [p_BD]			+10% -10%
✖Probability of Failure is the likelihood of losing an event.ⓘ Probability of Failure [q]			+10% -10%
✖Number of Independent Bernoulli Trials is the total number of consecutive and identical experiments with two possible outcomes that are conducted without any influence or dependency on each other.ⓘ Number of Independent Bernoulli Trials [n_Bernoulli]			+10% -10%

✖Geometric Probability Distribution Function is the probability of achieving the first success in a sequence of independent Bernoulli trials, where each trial has a constant probability of success.ⓘ Geometric Distribution [P_Geometric]

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Geometric Distribution

Formula

`"P"_{"Geometric"} = "p"_{"BD"}*"q"^("n"_{"Bernoulli "})`

Example

`"0.002458"="0.6"*("0.4")^("6")`

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Geometric Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Geometric Probability Distribution Function = Probability of Success in Binomial Distribution*Probability of Failure^(Number of Independent Bernoulli Trials)
P_Geometric = p_BD*q^(n_Bernoulli)
This formula uses 4 Variables

Variables Used

Geometric Probability Distribution Function - Geometric Probability Distribution Function is the probability of achieving the first success in a sequence of independent Bernoulli trials, where each trial has a constant probability of success.
Probability of Success in Binomial Distribution - Probability of Success in Binomial Distribution is the likelihood of winning an event.
Probability of Failure - Probability of Failure is the likelihood of losing an event.
Number of Independent Bernoulli Trials - Number of Independent Bernoulli Trials is the total number of consecutive and identical experiments with two possible outcomes that are conducted without any influence or dependency on each other.

STEP 1: Convert Input(s) to Base Unit

Probability of Success in Binomial Distribution: 0.6 --> No Conversion Required
Probability of Failure: 0.4 --> No Conversion Required
Number of Independent Bernoulli Trials: 6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_Geometric = p_BD*q^(n_Bernoulli) --> 0.6*0.4^(6)

Evaluating ... ...

P_Geometric = 0.0024576

STEP 3: Convert Result to Output's Unit

0.0024576 --> No Conversion Required

FINAL ANSWER

0.0024576 ≈ 0.002458 <-- Geometric Probability Distribution Function

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 6 Geometric Distribution Calculators

Geometric Distribution

Go Geometric Probability Distribution Function = Probability of Success in Binomial Distribution*Probability of Failure^(Number of Independent Bernoulli Trials)

Standard Deviation of Geometric Distribution

Go Standard Deviation in Normal Distribution = sqrt(Probability of Failure in Binomial Distribution/(Probability of Success^2))

Variance of Geometric Distribution

Go Variance of Data = Probability of Failure in Binomial Distribution/(Probability of Success^2)

Variance in Geometric Distribution

Go Variance of Data = (1-Probability of Success)/(Probability of Success^2)

Mean of Geometric Distribution given Probability of Failure

Go Mean in Normal Distribution = 1/(1-Probability of Failure in Binomial Distribution)

Mean of Geometric Distribution

Go Mean in Normal Distribution = 1/Probability of Success

Geometric Distribution Formula

Geometric Probability Distribution Function = Probability of Success in Binomial Distribution*Probability of Failure^(Number of Independent Bernoulli Trials)
P_Geometric = p_BD*q^(n_Bernoulli)

What is Probability in Mathematics?

In Mathematics, Probability theory is the study of chances. In real life, we predict chances depending on the situation. But Probability theory is bringing a mathematical foundation for the concept of Probability. For example, if a box contain 10 balls which include 7 black balls and 3 red balls and randomly chosen one ball. Then the Probability of getting red ball is 3/10 and Probability of getting black ball is 7/10. When coming to statistics, Probability is like the back bone of statistics. It has a wide application in decision making, data science, business trend studies, etc.

What is Geometric Distribution?

A Geometric Distribution is a probability distribution for a discrete random variable that describes the number of Bernoulli trials (experiments with only two possible outcomes, such as success or failure) that must be conducted in order for a success to occur. The probability of success in each trial is denoted as "p" and is a parameter of the distribution. The probability of the k-th trial being the first success is given by the probability mass function: P(X=k) = ((1-p)^(k-1))*p The Geometric Distribution is a special case of the negative binomial distribution. It is used in modeling the number of failures before the first success in a sequence of Bernoulli trials.

How to Calculate Geometric Distribution?

Geometric Distribution calculator uses Geometric Probability Distribution Function = Probability of Success in Binomial Distribution*Probability of Failure^(Number of Independent Bernoulli Trials) to calculate the Geometric Probability Distribution Function, The Geometric Distribution formula is defined as the probability of achieving the first success in a sequence of independent Bernoulli trials, where each trial has a constant probability of success. Geometric Probability Distribution Function is denoted by P_Geometric symbol.

How to calculate Geometric Distribution using this online calculator? To use this online calculator for Geometric Distribution, enter Probability of Success in Binomial Distribution (p_BD), Probability of Failure (q) & Number of Independent Bernoulli Trials (n_Bernoulli) and hit the calculate button. Here is how the Geometric Distribution calculation can be explained with given input values -> 0.157286 = 0.6*0.4^(6).

FAQ

What is Geometric Distribution?

The Geometric Distribution formula is defined as the probability of achieving the first success in a sequence of independent Bernoulli trials, where each trial has a constant probability of success and is represented as P_Geometric = p_BD*q^(n_Bernoulli) or Geometric Probability Distribution Function = Probability of Success in Binomial Distribution*Probability of Failure^(Number of Independent Bernoulli Trials). Probability of Success in Binomial Distribution is the likelihood of winning an event, Probability of Failure is the likelihood of losing an event & Number of Independent Bernoulli Trials is the total number of consecutive and identical experiments with two possible outcomes that are conducted without any influence or dependency on each other.

How to calculate Geometric Distribution?

The Geometric Distribution formula is defined as the probability of achieving the first success in a sequence of independent Bernoulli trials, where each trial has a constant probability of success is calculated using Geometric Probability Distribution Function = Probability of Success in Binomial Distribution*Probability of Failure^(Number of Independent Bernoulli Trials). To calculate Geometric Distribution, you need Probability of Success in Binomial Distribution (p_BD), Probability of Failure (q) & Number of Independent Bernoulli Trials (n_Bernoulli). With our tool, you need to enter the respective value for Probability of Success in Binomial Distribution, Probability of Failure & Number of Independent Bernoulli Trials and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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