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lector57 t1_j23lvi7 wrote

The coin tosses is your random experiment.

There are several possible results: 0, 1, 2,3 heads.

The number of heads obtained is the random variable. It's not fixed, you don't know the value until you perform the actual experiment.

The probability distribution is a formula that gives you the probability for each value.

So "what is the probability of obtaining 2 heads in 3 tosses" is exactly the same question as asking the value of the distribution (that is, probability mass function) when X=2

This is similar as in algebra... You have a function, for example f(x)=x² and you can ask it's value for any given x. For example when x=2, the function takes value 4

If you wanted to know the probability of getting no heads, if X="number of heads" is your random variable, you substitute X=0 on the appropriate mass function for this kind of problem

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Independent-Office80 OP t1_j23mkfi wrote

So they are just different representations of the same concept?

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lector57 t1_j23nv4r wrote

Like in algebra

x² is a function. A formula. X is the variable

Substitute x=2 and you get a value

In prob the random variable X can take different values.

The mass function is a formula. Substitute a specific value of X and you get the probability of obtaining the result X in the experiment

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Independent-Office80 OP t1_j23o0gg wrote

Oh. I get that now. Thanks. Could you elaborate on the inner workings of the PMF? Like, how it’s calculated on the inside? Thanks!

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lector57 t1_j23o467 wrote

It depends on the experiment/situation

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Independent-Office80 OP t1_j23o84h wrote

Oh. Doesn’t really explain much. But thanks a lot for taking your time to explain the previous. Means alot!

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