proper use of rand for coin toss

Hi,

This has been bugging me for a while. If I want to simulate a coin
toss using rand, what's the appropriate logical expression for
deciding between heads and tails?

coin = rand
if coin <0.5
toss = heads
else
toss = tails
end

But this biases toward tails w/the implied >= 0.5.

Looking at the help for rand, it doesn't appear to matter since rand
returns an even number of possible cases. But if rand was continuous
between 0 and 1 inclusive, what would be the appropriate test for
heads and tails?

Thanks,

-Chris

 

In theory, it's irrelevant since the x = 0.5 is an event with probability
zero.

 

if coin == 0.5
disp('Omigod! The coin landed on its edge!')'
end

Cheers,
Brett

 

Yes,

Just to confirm this I'm trying

for i=1:Inf
if (rand==0.5)
disp('Wah Hey!')
end;
end

I wonder how many Wah Heys I'll get?

Murphy

 

If it were continuous then the probability of obtaining 0.5 exactly
would be zero

Just resample if you obtain 0.5 exactly.

 

Murphy...you fail to appreciate the subtleties of ML. I'm curious how
much time this will save you:

tic;
count = 0;
for ii=1:inf
if rand == 0.5, count = count+1; end
end
t1=toc

tic
a = rand(Inf,1);
count = sum(a==0.5);
t2 = toc

Anxious to get the results...
Brett

 

[snip stuff regarding P(rand==0.5)]

My bet is on P(rand==0.5) = 2^-51.

I also guess that rand cannot, ever, return 1, exactly. Or maybe not zero.
If one of those is the case, then the r.v. is being generated over
(0,1]
or
[0,1)
in which case one should one should for heads,
(0,0.5]
or
[0,0.5),
respectively.
respectfully,
Aj

 

Well, rand only returns stuff between (0,1), so I'll bet instead on
eps(.5) = 1.11e-16. When rand tries to return 0.5 + x, it would
return 0.5 for x < 1.11e-16.

On the other hand 0.5 is an exponent boundary, so 0.5 - x is different
for x > 5.55e-17

In R14, help rand says:

This generator can generate all the floating point numbers in the
closed interval [2^(-53), 1-2^(-53)]. Theoretically, it can generate
over 2^1492 values before repeating itself.


So 0.5 is EXACTLY halfway between the extremes. The only error will
be if MATLAB wants 0.5 - x, x<5.55e-17, since that will look like 0.5.

I think?