Impact of transforming (scaling and shifting) random variables | AP Statistics | Khan Academy
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- เผยแพร่เมื่อ 1 ส.ค. 2017
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Linear transformations (addition and multiplication of a constant) and their impacts on center (mean) and spread (standard deviation) of a distribution.
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My stats teacher is the worst at explaining things- this was perfect, thank you
Oh my god, mine too.
same bro
Thanks for this one.
It is perfectly explained
Thanks so much for this video, amazing work. - coming from a IB DP Math Application student!
Showing the shifted curve on the same chart is confusing. The new curve no longer has the x-variable along the abscissa; it now has the y-variable. It should be on its own chart.
Why am I here im still on the qudratic formula thingy😂
High bro
Hi, thanks for the video! I have one doubt though, when we add K to Y(x), we get Y = X + K and I think that K should lift the bell curve up, not to move it to the right as presented at 2:24, or am I crazy?
you are correct, guess he wasn't focusing on that
It is correct. If you lifted the entire probability density function up by k, the integral of the probabilities would be greater than 1, which is not allowed.
What's happening here with the addition is (using his example of the heights of people walking out of a mall) putting everyone on stilts of height k inches. All it does is moves the entire curve upward by k units.
@@orengordon7921 No. You can't just lift the PDF. The integral of the probabilities would no longer be equal to 1.
The variable X is on the x-axis, so if you add something to X, it will slide along the x-axis
Hi thanks for the video. I have a question related to Var of Y
Isn't it k^2 * VarX ? In your video you say that VarY = k * VarX but I think you are missing the k squared.
If X is normal, and you have Y = aX + b then:
Mean(Y) = a* Mean(X) + b
Var(Y) = a^2 * Var(X)
Thanks in advance
Sebastián Gutiérrez Ik this is way gone but the sigma is standard deviation and not variance
@@CHIEFMURRY understood! Thanks! As is SD in both sides of the = sign, it isn't squared . Thanks!
Is A = X + X not the same thing as B = 2*X ?
the standard deviation of A = ( sigma(X)^2 + sigma(X)^2 )^(1/2)
but the standard deviation of B = 2 * sigma(X)
Why are these different?
Where did you get the formula for A's standard deviation?