Metallideth

March 9th 2011, 06:55 PM

I'm completely lost on this one.

If X is N(μ,σ^2), show that Y = aX + b is N(aμ + b, (a^2)(σ^2)), a is not equal to 0. Hint: Find the distribution function P(Y less than y) of Y, and in the resulting integral, let w = ax + b, or, equivalently, x = (w-b)/a

If I do the substitution, the integral is taken from negative infinity to y. That's all fine and good, but then the expression above the "e" term becomes awful, and I see no way to simplify it.

If X is N(μ,σ^2), show that Y = aX + b is N(aμ + b, (a^2)(σ^2)), a is not equal to 0. Hint: Find the distribution function P(Y less than y) of Y, and in the resulting integral, let w = ax + b, or, equivalently, x = (w-b)/a

If I do the substitution, the integral is taken from negative infinity to y. That's all fine and good, but then the expression above the "e" term becomes awful, and I see no way to simplify it.