Real life example of a continuous random variable.

Question

Let $X$ = number of heads if two fair coins are tossed simultaneously, and $TT = 0, HT=TH=1, HH=2$.

Then we have $Range = {0,1,2}$

the r.v. can take values 0,1, and 2.

Can someone give me a specific and to-the-point real-life example of a Continuous r.v. as is given in the above example of a discrete case?

@Infiaria, okay. go ahead and represent them as an experiment, events, r.v., and a range. — user366312, Feb 25 '19 at 13:53
Experiment: select two humans at random. experiment: weigh them, Range: (as weighed). — L. Scott Johnson, Feb 25 '19 at 13:54
If you want to stick to coins: flip two coins simultaneously. Record their "hang time" (the time elapsed from beginning of flip to when they come to rest). — L. Scott Johnson, Feb 25 '19 at 13:55
@L.ScottJohnson, in that case, should the outcome be considered as a pair of two real values, or sum of two real values? — user366312, Feb 25 '19 at 13:57
@user366312: since the original example shows adding (T=0, H=1), the parallel would be to add them here as well. — L. Scott Johnson, Feb 25 '19 at 13:59
@L.ScottJohnson, good. we are on target. but, what would be the range of the r.v.? — user366312, Feb 25 '19 at 14:01
@user366312 Twice the minimum hang time and twice the maximum hang time. — L. Scott Johnson, Feb 25 '19 at 14:04
@L.ScottJohnson, hmm... that doesn't quite match the discrete case as we had a concrete range there [0,1,2]. — user366312, Feb 25 '19 at 14:05
If you don't like hang time, try cutting the coins and the side to the right of the blade. Then the range will (0,1). And add the portions. — L. Scott Johnson, Feb 25 '19 at 14:06

score 0 · Answer 1 · answered Feb 25 '19 at 14:15

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Let X = total mass of coins left when two coins, each of mass 1, have a portion (between 0% and 100%) cut away. Then we have a range of (0,2). The r.v can take values between (0,2).

answered Feb 25 '19 at 14:15

L. Scott Johnson

191

What kind of distribution would it be and why? – user366312 Feb 25 '19 at 14:21
See https://math.stackexchange.com/questions/357672/density-of-sum-of-two-uniform-random-variables-0-1 – L. Scott Johnson Feb 25 '19 at 14:40
And see figure 7.2 in https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter7.pdf – L. Scott Johnson Feb 25 '19 at 14:42
What would be the PDF for this example? – user366312 Feb 25 '19 at 18:51

Real life example of a continuous random variable.

1 Answers1