help( dexp )

y.grid <- seq( 0, 15, length = 500 )

lambda <- 0.25

# quantile result from document camera notes:

print( y.median <- - log( 1 - 0.5 ) / lambda )

# [1] 2.772589

par( mfrow = c( 1, 1 ) )

plot( y.grid, dexp( y.grid, lambda ), type = 'l',
  lwd = 2, xlab = 'Possible Y Values', ylab = 'Density',
  main = 'Exponential PDF (lambda = 0.25)' )

abline( v = 0, lwd = 2 )

abline( h = 0, lwd = 2 )

abline( v = 2.772589, lwd = 2, col = 'red' )

text( 4.5, 0.2, 'median (2.77)', col = 'red' )

par( mfrow = c( 3, 1 ) )

plot( y.grid, dexp( y.grid, lambda ), type = 'l',
  lwd = 2, xlab = 'Possible Y Values', ylab = 'Density',
  main = 'Exponential PDF (lambda = 0.25)' )

abline( v = 0, lwd = 2 )

abline( h = 0, lwd = 2 )

abline( v = 2.772589, lwd = 2, col = 'red' )

text( 4.5, 0.2, 'median (2.77)', col = 'red', cex = 1.25 )

plot( y.grid, 1 - exp( - lambda * y.grid ), type = 'l',
  lwd = 2, xlab = 'Possible Y Values', ylab = 'CDF',
  main = 'Exponential CDF (lambda = 0.25)' )

abline( v = 0, lwd = 2 )

abline( h = 0, lwd = 2 )

abline( v = 2.772589, lwd = 2, col = 'red' )

abline( h = 0.5, lwd = 2, col = 'red')

text( 4.5, 0.2, 'median (2.77)', col = 'red', cex = 1.25 )

p.grid <- seq( 0.001, 0.999, length = 500 )

plot( p.grid, - log( 1 - p.grid ) / lambda, type = 'l',
  lwd = 2, xlab = 'Quantiles', ylab = 'Inverse CDF',
  main = 
  'Quantile Function (Inverse CDF) for Exponential (lambda = 0.25)' )

abline( h = 2.772589, lwd = 2, col = 'red' )

abline( v = 0.5, lwd = 2, col = 'red')

text( 0.1, 7.5, 'median (2.77)', col = 'red', cex = 1.25 )