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Topi
When the lecturer is talking about positive values why doesn't he use squares? By definition if you have order in the set (like reals) then positive values are greater than zero and all squares are greater than or equivalent to zero. So you don't need to point that e^px p has to be positive if you write it as e^p^2x. Hope you understant that; it's e to the power of p squared times x. p squared is guaranteed to be positive if it's not zero.
Which lecture are you talking about?