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<p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none">Hello Professor,</span></p>
<p class="gmail-p2" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;min-height:14px"><span class="gmail-s1" style="font-kerning:none"></span><br></p>
<p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none">I just saw the final grades released, and I have a small complaint about the grading policy you’ve adopted.</span></p>
<p class="gmail-p2" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;min-height:14px"><span class="gmail-s1" style="font-kerning:none"></span><br></p>
<p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none">After some calculation using the formula A = 0.8E + 0.2min(H,E); E = (3M + 5F)/8, I figured out that one can never get an A+ if he/she did the last question in the midterm wrong, even though he/she get 100% in HW and final. </span></p>
<p class="gmail-p2" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;min-height:14px"><span class="gmail-s1" style="font-kerning:none"></span><br></p>
<p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none">This hardly seems fair to me:</span></p>
<p class="gmail-p2" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;min-height:14px"><span class="gmail-s1" style="font-kerning:none"></span><br></p>
<p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none">1) The final grade of this course should not be contingent upon one single question.</span></p>
<p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none">2) The last question in the midterm is easy after we learned the product rule, which we had not at that time.</span></p>
<p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none">3) Many of our classmates (including me) are still confused about why the “common mistakes answers” for that question is wrong. You claimed that the function </span><img alt="f(t,W_t)=e^{-\lambda W_t}\int_0^t e^{\lambda W_s} dW_s" title="f(t,W_t)=e^{-\lambda W_t}\int_0^t e^{\lambda W_s} dW_s" class="va_li" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09f(t,W%5Ft)=e%5E{-%5Clambda%09W%5Ft}%5Cint%5F0%5Et%09e%5E{%5Clambda%09W%5Fs}%09dW%5Fs" id="l0.5806574166449716" style="display: inline; vertical-align: -5.867px;" height="22" width="209"> is not differentiable in time, but no further discussion. In fact, in my opinion, we can not adopt Ito's lemma here simply because <img alt="f(t,x)=e^{-\lambda x}\int_0^t e^{\lambda W_s}dW_s" title="f(t,x)=e^{-\lambda x}\int_0^t e^{\lambda W_s}dW_s" class="gmail-va_li" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09f(t,x)=e%5E{-%5Clambda%09x}%5Cint%5F0%5Et%09e%5E{%5Clambda%09W%5Fs}dW%5Fs" id="gmail-l0.8537435154740036" height="22" width="187" style="display: inline; vertical-align: -5.867px;"> is not a deterministic function in t and x.</p>
<p class="gmail-p2" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;min-height:14px"><span class="gmail-s1" style="font-kerning:none"></span><br></p>
<p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none">I would appreciate it if you could reconsider the grading policy to taking the issue I’ve mentioned into account. Otherwise if you don't accept my point, I hope you can give some detailed explanation on the last question in midterm. Thank you very much, and have a wonderful holiday!</span></p><p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none"><br></span></p><p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none">Best regards,</span></p><p class="gmail-p1" style="margin:0px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica"><span class="gmail-s1" style="font-kerning:none">Ze Yang</span></p></div>