# statistics best point estimation

Following table shows the usage of various symbols used in Statistics

## Capitalization

Generally lower case letters represent the sample attributes and capital case letters are used to represent population attributes.

• $P$ – population proportion.
• $p$ – sample proportion.
• $X$ – set of population elements.
• $x$ – set of sample elements.
• $N$ – set of population size.
• $N$ – set of sample size.

## Greek Vs Roman letters

Roman letters represent the sample attributs and greek letters are used to represent Population attributes.

• $\mu$ – population mean.
• $\bar x$ – sample mean.
• $\delta$ – standard deviation of a population.
• $s$ – standard deviation of a sample.

## Population specific Parameters

Following symbols represent population specific attributes.

• $\mu$ – population mean.
• $\delta$ – standard deviation of a population.
• ${\mu}^2$ – variance of a population.
• $P$ – proportion of population elements having a particular attribute.
• $Q$ – proportion of population elements having no particular attribute.
• $\rho$ – population correlation coefficient based on all of the elements from a population.
• $N$ – number of elements in a population.

## Sample specific Parameters

Following symbols represent population specific attributes.

• $\bar x$ – sample mean.
• $s$ – standard deviation of a sample.
• ${s}^2$ – variance of a sample.
• $p$ – proportion of sample elements having a particular attribute.
• $q$ – proportion of sample elements having no particular attribute.
• $r$ – population correlation coefficient based on all of the elements from a sample.
• $n$ – number of elements in a sample.

## Linear Regression

• $B_0$ – intercept constant in a population regression line.
• $B_1$ – regression coefficient in a population regression line.
• ${R}^2$ – coefficient of determination.
• $b_0$ – intercept constant in a sample regression line.
• $b_1$ – regression coefficient in a sample regression line.
• $^{s}b_1$ – standard error of the slope of a regression line.

## Probability

• $P(A)$ – probability that event A will occur.
• $P(A|B)$ – conditional probability that event A occurs, given that event B has occurred.
• $P(A’)$ – probability of the complement of event A.
• $P(A \cap B)$ – probability of the intersection of events A and B.
• $P(A \cup B)$ – probability of the union of events A and B.
• $E(X)$ – expected value of random variable X.
• $b(x; n, P)$ – binomial probability.
• $b*(x; n, P)$ – negative binomial probability.
• $g(x; P)$ – geometric probability.
• $h(x; N, n, k)$ – hypergeometric probability.

## Permutation/Combination

• $n!$ – factorial value of n.
• $^{n}P_r$ – number of permutations of n things taken r at a time.
• $^{n}C_r$ – number of combinations of n things taken r at a time.

## Set

• $A \Cap B$ – intersection of set A and B.
• $A \Cup B$ – union of set A and B.
• $\{ A, B, C \}$ – set of elements consisting of A, B, and C.
• $\emptyset$ – null or empty set.

## Hypothesis Testing

• $H_0$ – null hypothesis.
• $H_1$ – alternative hypothesis.
• $\alpha$ – significance level.
• $\beta$ – probability of committing a Type II error.

## Random Variables

• $Z$ or $z$ – standardized score, also known as a z score.
• $z_{\alpha}$ – standardized score that has a cumulative probability equal to $1 – \alpha$.
• $t_{\alpha}$ – t statistic that has a cumulative probability equal to $1 – \alpha$.
• $f_{\alpha}$ – f statistic that has a cumulative probability equal to $1 – \alpha$.
• $f_{\alpha}(v_1, v_2)$ – f statistic that has a cumulative probability equal to $1 – \alpha$ and $v_1$ and $v_2$ degrees of freedom.
• $X^2$ – chi-square statistic.

## Summation Symbols

• $\sum$ – summation symbol, used to compute sums over a range of values.
• $\sum x$ or $\sum x_i$ – sum of a set of n observations. Thus, $\sum x = x_1 + x_2 + … + x_n$.

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