Point Estimation

$\bullet$What is point estimation?
Example:
$\bullet$ Bevan, Kullberg, and Rice ( 1979) studied random fluctuations of current across a muscle cell membrane. The cell membrane contained a large number of channels, which opened and closed at random and were assumed to operate independently. The net current resulted from ions flowing through open channels.
$\bullet$ They obtained $49,152$ observations of the net current, $x_{1}, \ldots, x_{49152}$
$\bullet$ It seems appropriate to model the net current data,$X_{1}, \ldots, X_{49152}i.i.d. N\left(\mu, \sigma^{2}\right),$ where $\mu$ and $\sigma^{2}$ represent the mean and variance of net
Quiestion: how to use the observed data, $x_{1}, \ldots, x_{49152}$ to gain knowledge about the values of $\mu$ and $\sigma^{2} ?$

$\underline{Def:}$(procedure of fitting a particular distribution to data)
1.observed data:$\underline{x_1,x_2,\dots,x_n}$
2.statistical modeling:

巴特西

Point Estimation

Point Estimation

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