Merge pull request CamDavidsonPilon#230 from zapakh/master

Use possessive 'its' where appropriate

Author: CamDavidsonPilon

Chapter3_MCMC/IntroMCMC.ipynb

@@ -1065,7 +1065,7 @@
      "source": [
       "One way to think of autocorrelation is \"If I know the position of the series at time $s$, can it help me know where I am at time $t$?\" In the series $x_t$, the answer is No. By construction, $x_t$ are random variables. If I told you that $x_2 = 0.5$, could you give me a better guess about $x_3$? No.\n",
       "\n",
-      "On the other hand, $y_t$ is autocorrelated. By construction, if I knew that $y_2 = 10$, I can be very confident that $y_3$ will not be very far from 10. Similarly, I can even make a (less confident guess) about $y_4$: it will probably not be near 0 or 20, but a value of 5 is not too unlikely. I can make a similar argument about $y_5$, but again, I am less confident. Taking this to it's logical conclusion, we must concede that as $k$, the lag between time points, increases the autocorrelation decreases. We can visualize this:\n"
+      "On the other hand, $y_t$ is autocorrelated. By construction, if I knew that $y_2 = 10$, I can be very confident that $y_3$ will not be very far from 10. Similarly, I can even make a (less confident guess) about $y_4$: it will probably not be near 0 or 20, but a value of 5 is not too unlikely. I can make a similar argument about $y_5$, but again, I am less confident. Taking this to its logical conclusion, we must concede that as $k$, the lag between time points, increases the autocorrelation decreases. We can visualize this:\n"
      ]
     },
     {

Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb

@@ -72,7 +72,7 @@
       "\n",
       "Below is a diagram of the Law of Large numbers in action for three different sequences of Poisson random variables. \n",
       "\n",
-      " We sample `sample_size = 100000` Poisson random variables with parameter $\\lambda = 4.5$. (Recall the expected value of a Poisson random variable is equal to it's parameter.) We calculate the average for the first $n$ samples, for $n=1$ to `sample_size`. "
+      " We sample `sample_size = 100000` Poisson random variables with parameter $\\lambda = 4.5$. (Recall the expected value of a Poisson random variable is equal to its parameter.) We calculate the average for the first $n$ samples, for $n=1$ to `sample_size`. "
      ]
     },
     {

Chapter6_Priorities/Priors.ipynb

@@ -1272,7 +1272,7 @@
      "source": [
       "(Plots like these are what inspired the book's cover.)\n",
       "\n",
-      "What can we say about the results above? Clearly TSLA has been a strong performer, and our analysis suggests that it has an almost 1% daily return! Similarly, most of the distribution of AAPL is negative, suggesting that it's *true daily return* is negative.\n",
+      "What can we say about the results above? Clearly TSLA has been a strong performer, and our analysis suggests that it has an almost 1% daily return! Similarly, most of the distribution of AAPL is negative, suggesting that its *true daily return* is negative.\n",
       "\n",
       "\n",
       "You may not have immediately noticed, but these variables are a whole order of magnitude *less* than our priors on them. For example, to put these one the same scale as the above prior distributions:"