Geometric Distribution: Finding Specific p Value for Mean Calculation

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SUMMARY

The discussion centers on calculating the parameter p of a geometric distribution given a mean of 0.6. The probability generating function (p.g.f.) is defined as $$q/(1-ps)$$, where $$q$$ is (1 - p) and $$s$$ is a dummy variable. To find p, the relationship between the mean and p is established as $$mean = q/p$$, leading to the equation $$0.6 = (1-p)/p$$. Solving this equation yields the specific value of p for the geometric distribution.

PREREQUISITES
  • Understanding of geometric distribution and its properties
  • Familiarity with probability generating functions (p.g.f.)
  • Basic algebra for solving equations
  • Knowledge of mean calculations in probability theory
NEXT STEPS
  • Study the derivation of the probability generating function for different distributions
  • Learn how to manipulate and solve equations involving probabilities
  • Explore applications of geometric distribution in real-world scenarios
  • Investigate the relationship between mean, variance, and parameters in probability distributions
USEFUL FOR

Students studying probability theory, statisticians, and anyone interested in understanding geometric distributions and their applications in real-world problems.

umzung
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Homework Statement
The number of items bought by each customer entering a bookshop is a random variable X that has a geometric distribution starting at 0 with mean 0.6.
Find the value of the parameter p of the geometric distribution, and hence write down the probability generating function of X.
Relevant Equations
$$q/(1-ps)$$
I know the p.g.f. of X is $$q/(1-ps)$$ and that the mean is $$p/q$$, but how do I find a specific value for p here?
 
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umzung said:
Homework Statement:: The number of items bought by each customer entering a bookshop is a random variable X that has a geometric distribution starting at 0 with mean 0.6.
Find the value of the parameter p of the geometric distribution, and hence write down the probability generating function of X.
Homework Equations:: $$q/(1-ps)$$

I know the p.g.f. of X is $$q/(1-ps)$$ and that the mean is $$p/q$$, but how do I find a specific value for p here?

What are ##p, q## and ##s## here?
 
PeroK said:
What are ##p, q## and ##s## here?
$$p$$ is the probability, $$q$$ is (1 - probability) and $$s$$ is a dummy variable, not a random variable.
 
umzung said:
$$p$$ is the probability, $$q$$ is (1 - probability) and $$s$$ is a dummy variable, not a random variable.
Okay, so the mean is ##q/p = (1-p)/p##. Do you know the mean in this case?
 
Got it, thanks.
 

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