Register to reply

Binomial distribution

by aaaa202
Tags: binomial, distribution
Share this thread:
aaaa202
#1
Feb29-12, 02:50 AM
P: 1,005
Suppose you have a coin with 4 fair sides, flip it 5 times, and want to know the probability of 5 heads. This is
K(10,5) * (0.25)5 * (1-0.25)5 = K(10,5)*0.255*0.755
Or more generally for any binomially distributed outcome:

1) p(x=r) = pr*(1-p)n-r*K(n,r)

But also we must have that:

2) p(x=r) = K(n,r)/total combinations = K(n,r)/4n
How do you show that 1) and 2) are equivalent?
Phys.Org News Partner Science news on Phys.org
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display
alan2
#2
Feb29-12, 07:55 AM
P: 206
They're not equivalent. Your concept in 2) is not applicable in this case because the events are not equally likely.

Take for example a single coin flip of a fair coin where p=1-p=1/2. The probability of heads is the number of events resulting in heads divided by the total number of possible outcomes or 1/2. All events are equally likely. Now consider a weighted coin where p=3/4=p(heads). The number of ways to get heads is still 1 and the total number of possible outcomes is still 2 but p(heads) does not equal 1/2.
aaaa202
#3
Feb29-12, 01:31 PM
P: 1,005
hmm...

you were to suppose that each side was equally probable :)

alan2
#4
Feb29-12, 02:10 PM
P: 206
Binomial distribution

Ooops, I'm really sorry, you have a 4 side coin. My bad.

Anyway, your expressions are incorrect. I'm assuming only one side of the coin is heads. In that case, the probability of 5 heads is (0.25)^5=(1/4)^5.

Alternatively, the number of ways to get 5 heads is 1 and the number of possible outcomes is 4^5, so P(5 heads)=1/(4^5). Same result. Where did the 10 come from?


Register to reply

Related Discussions
Casio fx-9860G - calculating binomial coefficients and binomial distribution General Math 3
Relationship binomial distribution and central limit theorem + poission distribution Set Theory, Logic, Probability, Statistics 1
Poisson distribution and binomial distribution questions Linear & Abstract Algebra 1
How is the negative binomial the inverse of the binomial distribution? Set Theory, Logic, Probability, Statistics 1
Derivation of the probability distribution function of a binomial distribution General Math 2