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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


Independent-Office80 OP t1_j23mkfi wrote

So they are just different representations of the same concept?


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


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!


lector57 t1_j23o467 wrote

It depends on the experiment/situation


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!


barrycarter t1_j23nwys wrote

You're correct in thinking they are (almost) the same thing, but it's easier for average people (including people starting out in statistics) to think of "fair dice", "fair coin", "roulette wheel" or "what are the chances Ms Johnson has two boys..." versus something like "the discrete uniform distribution of {1, 2, 3, 4, 5, 6}" or "assume an independent binary process repeated 3 times..." or whatever.

So, why "(almost)"? Because, in the real world, there are no fair die, no fair coins (I believe a study recently showed that the way most people flip coins, the side that was up originally is more likely to be up after the flip), gender distribution at birth is unequal (more boys born than girls), and so on. There isn't even really such a thing as a random sample since we have no way to generate true randomness.

So, the whole coin/marbles/roulette wheel/etc thing is just a way to make statistics more accessible to the beginners and the average person