# Week 2 Quiz - issue with question

Available answers to Question 5 of my quiz do not make sense. None of them seem correct according to the formulas from the lecture. What does prime sign mean?

Sorry for posting the question, but answer is wrong anyway. Please delete it if not allowed.

As we learned, “exponentially weighted averages” is useful to see a trend from noisy data. As you see, given equations are;

v_0 = 0, \ \ \ v_t = \beta v_{t-1} + (1-\beta)\theta_t, \ \ \ \beta = 0.5

Let’s think about the case just using the above equation.

v_0 = 0 \\ v_1 = \beta v_0 + (1-\beta)\theta_1 = 0.5*0 + 0.5*10 = .... \\ v_2 = \beta v_1 + (1-\beta)\theta_2 = 0.5*v_1 + 0.5*10 = ....

Using “weights”, we calculate “temperature” for a trend analysis from yesterday and today’s temperature. I think you can get the answer from the above easily.

As we started with v_0 = 0, this trend curve started from a lower value since it is an exponentially weighted average of \theta_1 and 0. We need to think about a bias term.
Andrew proposed a following equation for Bias correction, \frac{v_t}{1-\beta^t} instead of vt.
So, the above equations are now;

v_0 = v_0^{corrected} = 0, \ \ \ v_t^{corrected} =\frac{ \beta v_{t-1}^{correctetd} + (1-\beta)\theta_t}{1-\beta^t}, \ \ \ \beta = 0.5

Then, you can calculate “temperature” just like we did without bias correction.

But, I realized that confusions may come from a “prime sign” that you pointed out. This is used in different ways in math, like “transpose”, “derivative”, .
In this case, I suppose this is either typo or problem in interpreting LaTex text in a browser. This must be “comma” to separate v_2 and v_2^{corrected}.