Hi,
I think the equation $p(\lambda | { x_n }{n=1}^N) = \frac{ 1}{p({ x_n }{n=1}^N )} p(\lambda) \prod_{n=1}^N p({ x_n }{n=1}^N | \lambda ) \propto p(\lambda) \prod{n=1}^N p( x_n | \lambda )$ should read $p(\lambda | { x_n }{n=1}^N) = \frac{ 1}{p({ x_n }{n=1}^N )} p(\lambda) \prod_{n=1}^N p(x_n | \lambda ) \propto p(\lambda) \prod_{n=1}^N p( x_n | \lambda )$ instead, i.e. the product should be over the individual data points