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6 votes
Accepted

Confusion about the probability of a continuous random variable at a given point

The question wording leaves a little bit of room for interpretation, but I would assume that they mean that the chosen battery lasts exactly 5 years. Not: after 5 years, it's still going. If you do as ...
Ruben van Bergen's user avatar
4 votes

What is the median of the minimum or maximum of multiple samples?

The cumulative distribution function $F_{(1)}$ for the minimum of $k$ draws from a distribution is $1-(1-F(x))^k$, the complement of the probability that all $k$ draws are above $x$. So the median for ...
Matt F.'s user avatar
  • 5,352
4 votes
Accepted

What is the median of the minimum or maximum of multiple samples?

Let the distribution function of the variable $X$ be $F.$ Given any number $y,$ the chance that the minimum of $k$ iid copies of $X$ exceeds $y$ is the chance that all of those $k$ values exceed $y.$ ...
whuber's user avatar
  • 329k
4 votes

Confusion about the probability of a continuous random variable at a given point

Ruben gave a very good answer with the lifespan of five years, exactly, which seems to be what the people who wrote the question wanted. But .... I think that's kind of a weird way to think of the ...
Peter Flom's user avatar
  • 125k
3 votes

When running a Bayesian mixed effects regression, if a random effect estimate has 95% CIs that include zero, should it be disregarded?

I never understood why people would choose to use Bayesian methods, only to fall back onto frequentist tendencies. In any case, my advice would be to make the decision by comparing models with and ...
Demetri Pananos's user avatar
2 votes

Confusion about the probability of a continuous random variable at a given point

Ruben and Peter Flom have given the relevant practical answers but I want to point out that conditioning on events with probability 0 is in fact not always a well defined undertaking. If you have no ...
Lukas Lohse's user avatar
  • 2,862
1 vote

Calculating the joint pdf of linearly dependent random variables $X$ and $Y=X$

As already explained in comments, there is no joint density in the plane, because all the probability mass of $(X, X)$ is concentrated on the diagonal $y=x$. There is a density on that diagonal, but ...
kjetil b halvorsen's user avatar

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