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Apr
9
comment Probability applied to economics
@ScottGoddard but the problem says that "$30\%$ of the professors who received this material adopted the book", so $(S,A) = 0.3 \times 0.8 = 0.24$!
Apr
9
comment Why does convexity of a function required the following
@user2654176 see the edit, this is equivalent to $f''>0$ (assume $f''$ exists).
Apr
9
comment Probability applied to economics
@ScottGoddard Looks like you evaluated incorrectly. What numbers did you get for each of the 4 sets, and how did you get them?
Apr
9
comment Why does convexity of a function required the following
@user2654176 I don't understand what you are asking.
Apr
9
comment Limits: $\lim_{x\to0^+}xe^\frac{-1}x$ and $\lim_{x\to0^-}xe^\frac{-1}x$
Can you please exhibit at least some attempt at solving the problem yourself? Then we can comment and give some hints. This is not the "society of people who do your homework for you."
Apr
9
comment What's the MLE of $\frac1\lambda$ for $f(x)=\frac1\lambda\exp − \frac x\lambda$?
Please clarify the equations in the text, they way it is phrased makes no sense to me.
Apr
9
comment Suppose $A, B$, and C are sets. Prove that $C\subset A\Delta B \Leftrightarrow C \subset A \cup B$ and $A \cap B \cap C = \emptyset $
@GabeCarr the phrase "the statement A ⋂ B ⋂ C must be an empty or null set" is wrong: $A \cap B \cap C$ is not a statement, and statements cannot be empty or null sets. What is meant to say is that the set $A \cap B \cap C$ is empty, i.e. $A \cap B \cap C = \emptyset$
Apr
9
comment What is the shortest way to write the number $1234567890$?
@DavisYoshida how do you denote $55_{64}$ by one digit -- rubik's notation is only good for base 36 (10 digits + 26 letters)?
Apr
9
comment What is the shortest way to write the number $1234567890$?
One approach is to find some relatively short base, and it shrinks fast, e.g. it is $499602D2_{16}$ (same 10 digits).
Apr
9
comment Evaluate the limit
@rubik Missed the all real numbers part, thank you
Apr
9
comment Suppose $A, B$, and C are sets. Prove that $C\subset A\Delta B \Leftrightarrow C \subset A \cup B$ and $A \cap B \cap C = \emptyset $
@GabeCarr not sure what you mean. The event $z \in X - Y = X \cap \bar{Y}$ happens if and only if $z \in X$ and $z \not \in Y$.
Apr
9
comment Probability of eight dice showing sum of 9, 10 or 11
Looks right to me
Apr
9
comment Evaluate the limit
Why cannot you have $$\psi(x) = 2 + \frac{1}{x} \to 2$$ instead? By this example it can converge to any limit...
Apr
9
comment Evaluate the limit
I don't understand what the second condition adds: since $t^2 < (t+1)^2$, we already know that $$\psi(t^2) > \psi(t^2+1) > \ldots > \psi\left((t+1)^2\right)$$
Apr
9
comment How to find maximum/minimum of $y=\frac{x(x^2-x+2)}{x^2-9}$?
@Cherufe both min and max are unbounded
Apr
9
comment Line integral segment of parabola
@user131040 please be more specific, i am not telling you the answer. But will comment on what you are doing exactly if you tell me the steps you took. What are you using for $x,y$ and which integral are you taking?
Apr
8
comment Line integral segment of parabola
@user131040 i thought the text specified this pretty clearly
Apr
8
comment Line integral segment of parabola
@user131040 You must express them in terms of $t$, as we defined when we parameterized the curve.
Apr
8
comment How to find maximum/minimum of $y=\frac{x(x^2-x+2)}{x^2-9}$?
@Cherufe As $x \to \pm \infty$ there cannot be problems with any finite values of $x$...
Apr
8
comment Is $(A+B)^2 = A^2 + B^2$ if $A$ and $B$ are matrices
Moreover, you proved OP's statement is true iff $AB = -BA$.