Typo fixes.
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@ -8692,7 +8692,7 @@
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"\n",
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"Now suppose that each value has a different probability of happening. Say 1 has an 80% chance of occurring, 3 has an 15% chance, and 5 has only a 5% chance. In this case we compute the expected value by multiplying each value of $x$ by the percent chance of it occurring, and summing the result. So for this case we could compute\n",
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"\n",
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"$$E[x] = 1\\times 0.8 + 3\\times 0.15 + 5 \\times 0.05 = 1.5$$\n",
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"$$E[x] = (1)(0.8) + (3)(0.15) + (5)(0.05) = 1.5$$\n",
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"\n",
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"Here I have introduced the standard notation $E[x]$ for the expected value of $x$.\n",
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@ -8750,8 +8750,8 @@
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"\n",
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"$$\n",
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"\\begin{aligned}\n",
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"COV(a,b) &= \\frac{1}{2}[(1-2)^2 + (3-2)^2] \\\\\n",
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"&= \\frac{1}{2}[(1+1] \\\\\n",
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"VAR(a) &= \\frac{1}{2}[(1-2)^2 + (3-2)^2] \\\\\n",
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"&= \\frac{1}{2}[1+1] \\\\\n",
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"&= 1\\end{aligned}$$\n",
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"\n",
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"\n",
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