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2d
comment Random vector with density on triangle and trapezoid
Regrettably, the calculations that you have included with your edit are incorrect beginning from the very first line. Perhaps trying my previous suggestion might help you figure out where you went astray.
2d
comment degree of generator polynomial $m(x)$
What dreadfully nonstandard notation! What book are you reading? The reason for the condition $\gcd(h,u) = 1$ is that the standard theory of cyclic codes assumes that there exists a $h$-th root of unity in the finite field $F_u$ or some extension field of $F_u$. But, $u = p^m$ for some prime $p$ and positive integer $m$, and in a field of characteristic $p$, no element can have multiplicative order that is a multiple of $p$. Thus, $\gcd(h,u) = 1$ means we are considering the standard theory. Without this restriction, each theorem would need to include special cases for codes for which $p|h$.
Feb
2
answered Does generator matrix of a code $C$ must have linearly independent rows?
Feb
2
comment Random vector with density on triangle and trapezoid
Begin by drawing a sketch of the plane with coordinate axes $x,y$ and mark on it the regions where the joint density has value $\frac 14$ and $\frac{9x}{184}$.
Feb
1
comment Joint distribution of two normal marginal distributions
Consider the case $k = 1$. Then, $X_n$ and $Y_n$ being marginally normal, say $N(0,1+\frac 1n)$, does not imply that $X_n$ and $Y_n$ are jointly normal. So, $X_n$ and $Y_n$ can each converge to standard normal $X$ and $Y$ but the joint distribution of $(X_n,Y_n)$ does not necessarily converge to the bivariate joint normal distribution of $(X,Y)$. For many examples of marginally normal random variables that are not jointly normal, see this answer on stats.SE.
Jan
29
comment A Binomial coefficient sequence
What, if any, is the relationship between $k$ and $r$?
Jan
29
comment Finding the conditional distribution of 2 dependent normal random variables
Asked simultaneously on stats.SE where it has received two answers.
Jan
28
revised Show that there is precisely one cyclic code C of length 4 and dimension 2. Write down all the codewords in C.
added 25 characters in body
Jan
28
answered Show that there is precisely one cyclic code C of length 4 and dimension 2. Write down all the codewords in C.
Jan
25
comment Conditional probability: compute $P(B)$ when $P(B|A), P(A'|B)$ and $P(A)$ are given
At the level of the question asked, just keep in mind two things: (i) You cannot add or subtract conditional probabilities unless the conditions are the same. $$P(A\cup B\mid C) = P(A\mid C)+P(B\mid C)-P(A\cap B\mid C)$$ is correct; $$P(B)=P(B\mid A)+P(B\mid A^c)\tag{1}$$ is not. (ii) $B\mid A$ and $B\mid A^c$ are not events, and you cannot claim that they are mutually exclusive because $A$ and $A^c$ are mutually exclusive. On the other hand, $B\cap A$ and $B\cap A^c$ are indeed events, and it is true that $$P(B)=P(B\cap A)+P(B\cap A ^c)=P(B\mid A)P(A)+P(B\mid A^c)P(A^c).\tag{2}$$
Jan
24
comment What is the expected value of cosine of a multivariate Gaussian?
Hint: $t^TX = \sum_i t_iX_i$ is a (univariate) Gaussian random variable $Y$ with mean $t^T\mu$ and variance $t^T\Sigma t$. So, can you figure out what $E[\cos Y]$ and $E[\sin Y]$ are? (See danimal's hint)
Jan
23
comment Probability that one chi-squared random variable is less than other chi-squared random variable
Thanks for accepting my hints as the answer. Yes, what you have written above is correct, but once again, you are missing the forest while carefully cutting down multiple trees. Since $Z$ and $W$ are identically distributed, $P(W>0)$ and $P(Z<0)$ are complementary probabilities: their sum is $1$. Thus, $P(X^2<Y^2)$ is necessarily of the form $2p(1-p)$ and so we need find only one probability. It is a standard result that for $T \sim N(a,b^2)$, $$P(T\leq c) = \Phi\left(\frac{c-a}{b}\right) = Q\left(\frac{a-c}{b}\right)$$ but working out the details one more time by hand is OK too.
Jan
21
awarded  Necromancer
Jan
20
answered If $P(ABC)=0.2$, are $A$ and $C$ mutually exclusive?
Jan
13
comment Compound Distribution — Uniform Distribution with Normally Distributed Parameters
What happens if $X > Y$? Are $X$ and $Y$ independent?
Jan
12
revised How to prove the independence of a variable that is the sum of two independent random variables
edited body
Jan
12
revised derivative of expected value with respect to parameter in both pdf and expectation
added 45 characters in body
Jan
12
answered derivative of expected value with respect to parameter in both pdf and expectation
Jan
7
comment derivative of expected value with respect to parameter in both pdf and expectation
Dang typo! It should have said $g(x)$ is not a random variable. I have no idea what $x_0$ and $x_T$ are; please explain.
Jan
7
comment derivative of expected value with respect to parameter in both pdf and expectation
$g(X)$ is not a random variable; $g(X)$ is. $x$ on the right is not the same as the $x$ on the left. $E(g(x))$ is just $g(x)$, plain and simple, and its derivative wrt $x$ is what you would get in Calculus 101.