CDF to PDF problem (probability)

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The discussion revolves around solving a problem related to converting a cumulative distribution function (CDF) to a probability mass function (PMF). The user calculates PMF values and attempts to ensure the total area under the curve equals one, leading to the conclusion that A must equal 1.7. However, there are questions about the behavior of the CDF as y approaches infinity and the graphical representation of the PMF. Additionally, the user seeks clarification on the formula for the expectation of a distribution. The conversation highlights the complexities involved in understanding the relationship between CDF and PMF.
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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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