Normal Distribution as Approximation to Binomial Distribution
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experiments = 1000 | |
visitors = 250 | |
conversion_rate = 0.3 | |
expected_conversions = visitors * conversion_rate | |
expected_sd = sqrt( visitors * conversion_rate * ( 1 - conversion_rate ) ) | |
sd_for_axis_range = 4.5 | |
axis_divisions = 5 | |
results = vector() | |
for ( experiment in 1:experiments ) { | |
conversions = 0 | |
for ( visitor in 1:visitors ) { | |
if ( runif( 1 ) <= conversion_rate ) { | |
conversions = conversions + 1 | |
} | |
} | |
results = c( results, conversions ) | |
} | |
par( oma = c( 0, 2, 0, 0 ) ) | |
axis_min = floor( ( expected_conversions - sd_for_axis_range * expected_sd ) / axis_divisions ) * axis_divisions | |
axis_max = ceiling( ( expected_conversions + sd_for_axis_range * expected_sd ) / axis_divisions ) * axis_divisions | |
hist( results, axes = FALSE, breaks = seq( axis_min, axis_max, by = 1 ), ylab = 'Probability', xlab = 'Conversions', freq = FALSE, col = '#4B85ED', main = 'Distribution of Results' ) | |
axis( side = 1, at = seq( axis_min, axis_max, by = axis_divisions ), pos = 0, col = "#666666", col.axis = "#666666", lwd = 1, tck = -0.015 ) | |
axis( side = 2, col = "#666666", col.axis = "#666666", lwd = 1, tck = -0.015 ) | |
curve( dnorm(x, mean = conversion_rate * visitors, sd = expected_sd ), add = TRUE, col = "red", lwd = 4 ) |
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