Timeline for Does joint probability apply when calculating likelihood with the binomial distribution?
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| Mar 13, 2022 at 22:05 | comment | added | Kirsten | So in summary, X is a Binomial RV and the 7 joint RVs are Bernoulli RVs.? | |
| Mar 13, 2022 at 20:44 | comment | added | Dilip Sarwate | @Kirsten Well, yes, $X$ is indeed a binomial random variable, but you are insisting on finding a joint distribution of $X$ and some other random variable. The outcomes of the experiment (the data) are the 7 answers and the joint distributions that you ought to be seeking are the joint distribution of the 7 answers, and not the joint distribution with something else. | |
| Mar 13, 2022 at 12:10 | comment | added | Kirsten | Thank you, but why is X not an RV? It looks like a "numerical description of the outcome of a statistical experiment." (though I now appreciate that the independent RVs in this problem must be the binary drink outcome ) britannica.com/science/statistics/… | |
| Mar 12, 2022 at 14:44 | comment | added | Dilip Sarwate | @Kirsten Repeat as often as needed till you have memorized it: "X is not a random variable". There are 7 independent random variables representing the 7 answers; these random variables take on value Orange with (unknown) probability $p$ and value Grape with probability $1-p$. 4 of the answers are known to have value Orange and 3 to have value Grape. Before asking for the choices, we know that the joint probability that 4 of these 7 random variables will have value Orange and 3 will have value Grape is $\binom 74p^4(1-p)^3$. Repeat again: "X is not a random variable". | |
| Mar 12, 2022 at 6:38 | comment | added | Kirsten | Thank you for the joint probability update. However looking at Wikipedia, a joint probability distribution involves two random variables. Surely we have only one here? that is X? Only X is mentioned in the Likelihood equation? Or is the other RV implied somehow as N-X? From your answer I guess it must be ... but surely N-X is not an RV indepentant of X? en.wikipedia.org/wiki/Joint_probability_distribution | |
| Mar 11, 2022 at 21:17 | history | edited | Dilip Sarwate | CC BY-SA 4.0 |
added 1958 characters in body
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| Mar 11, 2022 at 21:15 | vote | accept | Kirsten | ||
| Mar 11, 2022 at 18:17 | comment | added | Kirsten | Thank you for clearing my confusion about the wording. I also asked about how joint probability applies here. Should that be a separate question? | |
| Mar 11, 2022 at 15:00 | history | answered | Dilip Sarwate | CC BY-SA 4.0 |