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Instead of

f = lambda x, N: prod([P for x in range(1, N)])

use

f = lambda x, N: product(P, k, 1, N)

Also, maybe you want

P(x) = 1/sqrt((2*pi*sigma^2))*exp(-((x-mu)/sigma)^2/2)
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No.2 Revision

Instead In Sage, sum serves both for Python sums and for symbolic sums, but for products we have prod and product.

Declare an extra symbolic variable k, and instead of

f = lambda x, N: prod([P for x in range(1, N)])

use

f = lambda x, N: product(P, k, 1, N)

Also, maybe check your expression for P. Maybe you wantwant this instead:

P(x) = 1/sqrt((2*pi*sigma^2))*exp(-((x-mu)/sigma)^2/2)