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# Bivariate Distribution Formula

Bivariate Distribution is a quantitative (statistical) analysis, involving the analysis of two variables. This page contains the bivariate distribution formula to calculate the probability density function for the given values of X and Y percentiles. The Bivariate distribution analyzes empirical relationship between two variables. Bivariate normal distribution is the statistical distribution with probability density function, which depends upon correlation coefficient, and X and Y percentiles.

#### Formula:

Probability Density (f) = ( 1 / ( 2 π √ ( 1 - p2))) × ( e ( - ( x2 - 2pxy + y2)) / ( 2 ( 1 - p2)))

Where,

f = Probability Density
x = Percentile x
y = Percentile y
p = Correlation Coefficient

#### Related Calculator:

The bivariate distribution formula is useful in estimating the probability function of two random variables. Use our online bivariate calculator to efficiently calculate the density function and crosscheck your manual results.