lambda <- 0.5

upper <- 10

dpois( 0:upper, lambda )

# [1] 6.065307e-01 3.032653e-01 7.581633e-02 1.263606e-02 1.579507e-03 1.579507e-04
# [7] 1.316256e-05 9.401827e-07 5.876142e-08 3.264523e-09 1.632262e-10

# plot( 0:upper, dpois( 0:upper, lambda ), type = 'l',
#  xlab = 'y', ylab = 'P( Y = y )' )

plot( 0, 0, xlim = c( 0, upper ), 
  ylim = c( 0, max( dpois( 0:upper, lambda ) ) ), 
  xlab = 'y', ylab = 'P ( Y = y )', type = 'n' )

for ( i in 0:upper ) {

  segments( i, 0, i, dpois( i, lambda ), lwd = 2 )

}

lambda <- 1

dpois( 0:upper, lambda )

# [1] 3.678794e-01 3.678794e-01 1.839397e-01 6.131324e-02 1.532831e-02 3.065662e-03
# [7] 5.109437e-04 7.299195e-05 9.123994e-06 1.013777e-06 1.013777e-07

plot( 0, 0, xlim = c( 0, upper ), 
  ylim = c( 0, max( dpois( 0:upper, lambda ) ) ), 
  xlab = 'y', ylab = 'P ( Y = y )', type = 'n' )

for ( i in 0:upper ) {

  segments( i, 0, i, dpois( i, lambda ), lwd = 2 )

}

lambda <- 2

dpois( 0:upper, lambda )

# [1] 1.353353e-01 2.706706e-01 2.706706e-01 1.804470e-01 9.022352e-02 3.608941e-02
# [7] 1.202980e-02 3.437087e-03 8.592716e-04 1.909493e-04 3.818985e-05

plot( 0, 0, xlim = c( 0, upper ), 
  ylim = c( 0, max( dpois( 0:upper, lambda ) ) ), 
  xlab = 'y', ylab = 'P ( Y = y )', type = 'n' )

for ( i in 0:upper ) {

  segments( i, 0, i, dpois( i, lambda ), lwd = 2 )

}

lambda <- 3

dpois( 0:upper, lambda )

# [1] 0.0497870684 0.1493612051 0.2240418077 0.2240418077 0.1680313557 0.1008188134
# [7] 0.0504094067 0.0216040315 0.0081015118 0.0027005039 0.0008101512

plot( 0, 0, xlim = c( 0, upper ), 
  ylim = c( 0, max( dpois( 0:upper, lambda ) ) ), 
  xlab = 'y', ylab = 'P ( Y = y )', type = 'n' )

for ( i in 0:upper ) {

  segments( i, 0, i, dpois( i, lambda ), lwd = 2 )

}

par( mfrow = c( 2, 2 ) )