CDF to PDF problem (probability)

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asdf12312
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Homework Statement


Staircase graph of the CDF F_Y(y) of a random variable Y, with steps at y = 0, 2 and 3; the value 0.3 is marked after y = 0, 0.6 after y = 2, and the top level is labeled A.


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


Step plot of the CDF F_Y(y) of a discrete random variable: jumps to 0.3 at y = 0, to 0.6 at y = 2, and to A at y = 3, then flat; the question asks for A, the PMF and E[Y].
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)?