CDF to PDF problem (probability)

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SUMMARY

The discussion focuses on converting a cumulative distribution function (CDF) to a probability mass function (PMF) in a probability context. The user calculates specific PMF values: 0.3 for x=0, 0.3 for x=2, and A-0.6 for x=3, ultimately solving for A as 1.7. The area under the PMF curve is confirmed to equal 1, adhering to the integral property of probability distributions. The user also poses questions regarding the behavior of F(y) as y approaches infinity and the graphical representation of the PMF.

PREREQUISITES
  • Understanding of probability mass functions (PMF)
  • Knowledge of cumulative distribution functions (CDF)
  • Familiarity with integral calculus and area under curves
  • Basic concepts of expectation in probability distributions
NEXT STEPS
  • Study the relationship between CDF and PMF in discrete probability distributions
  • Learn about the properties of integrals in probability theory
  • Explore graphical representations of PMF and CDF
  • Investigate the calculation of expected values for different probability distributions
USEFUL FOR

Students studying probability theory, statisticians working with discrete distributions, and educators teaching concepts of PMF and CDF relationships.

asdf12312
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Homework Statement


photo_3.png


Homework Equations


integral from -inf to inf of fx(x)dx = 1, fx(x)=PMF

The Attempt at a Solution


I get values for probability function PMF of:
0.3, x=0
0.3, x=2
A-0.6, x=3

I guess I try to find area under curve of PMF which will be equal to 1. (0.3)(2) + (1/2)(1)(A-0.6-(0.3))=1 -> A=1.7
Am I doing it right?
 
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asdf12312 said:

Homework Statement


photo_3.png
Y

Homework Equations


integral from -inf to inf of fx(x)dx = 1, fx(x)=PMF

The Attempt at a Solution


I get values for probability function PMF of:
0.3, x=0
0.3, x=2
A-0.6, x=3

I guess I try to find area under curve of PMF which will be equal to 1. (0.3)(2) + (1/2)(1)(A-0.6-(0.3))=1 -> A=1.7
Am I doing it right?
Don't think so.

(a) what must be the value of F(y) for y → ∞?
(b) since PMF(y) = f(y) = (d/dy)F(y), how must the PMF graph look?
(c) what's the formula for expectation of a distribution f(y)?
 

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