Understanding the PMF of a Random Variable: A Brief Overview

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Understanding the probability mass function (PMF) of a random variable requires foundational knowledge, including the distinction between continuous and discrete probability distributions. The discussion emphasizes the importance of effort in learning, suggesting that users should engage with the material before seeking assistance. A recommendation is made to sketch the cumulative distribution function (CDF) to better grasp the concepts. The initial poster acknowledges limited progress and seeks a foundational answer for further questions. Engaging with these concepts is essential for a deeper understanding of probability theory.
flughafen
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Homework Statement
statistics
Relevant Equations
pmf
I am new to the topic so I do need your help here. Thanks in advance

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Hello @flughafen, :welcome: !

Unfortunately for you, PF requires an effort from you before we are allowed to assist. So: what have you got thus far ?
 
BvU said:
Hello @flughafen, :welcome: !

Unfortunately for you, PF requires an effort from you before we are allowed to assist. So: what have you got thus far ?

I haven't gotten much far yet. Just left it there, thinking that I could use the answer of this as base for other alike questions.
 
flughafen said:
I haven't gotten much far yet. Just left it there, thinking that I could use the answer of this as base for other alike questions.

Have you tried sketching the cdf as in part a? This should help you to see what's going on.
 
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Do you not at least know the difference between a "continuous" and a "discrete" probability distribution? That is one of the questions asked that you did not answer.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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