- #1
Ryoukomaru
- 55
- 0
An unbiased coin is tossed n times and X is the number of heads obtained. Write down an expression for the probability that X=r.
It looks so simple yet I can't figure it out.
Does it follow a binomial distribution ?
Then if
[tex]
X[/tex]~[tex]N (n,p)[/tex]
It follows
[tex]
P(X=r) = \left(
\begin{array}{cc}
n\\
r
\end{array}
\right)
\cdot p^r \cdot q^{n-1} [/tex]
where [tex]q=1-p[/tex]
But [tex] p=q=1/2
[/tex]
So the answer is
[tex]
P(X=r) = \left(
\begin{array}{cc}
n\\
r
\end{array}
\right)
\frac{1}{2}^{r+n-1}[/tex]
Am I right ?
P.S. First time using latex. It sure took long.
It looks so simple yet I can't figure it out.
Does it follow a binomial distribution ?
Then if
[tex]
X[/tex]~[tex]N (n,p)[/tex]
It follows
[tex]
P(X=r) = \left(
\begin{array}{cc}
n\\
r
\end{array}
\right)
\cdot p^r \cdot q^{n-1} [/tex]
where [tex]q=1-p[/tex]
But [tex] p=q=1/2
[/tex]
So the answer is
[tex]
P(X=r) = \left(
\begin{array}{cc}
n\\
r
\end{array}
\right)
\frac{1}{2}^{r+n-1}[/tex]
Am I right ?
P.S. First time using latex. It sure took long.