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I am a retired professor of electrical and computer engineering with a lifetime of experience teaching probability and statistics to undergraduates and error-correcting coding theory to graduate students.


7h
comment Probability of real roots
Why does $\Delta > 0$ result in integer roots? Real roots, yes; but integer roots?
13h
comment expectation lognormal and normal
Hint: try computing $E[Ye^{-X}]$ by first computing the conditional expectation $E[Ye^{-X}\mid Y = y]$. This should be easy to do since this is just $yE[e^{-X}\mid Y = y]$ and you know, I hope, that conditioned on the value of $Y$, the conditional distribution of $X$ is normal. Thus you should be getting something related to the MGF of a normal random variable of known mean and variance. Then, use the law of iterated expectation to get $E[Ye^{-X}] = E[E[Ye^{-X}]]$.
1d
reviewed Approve suggested edit on Normal Distribution Worded Problem
1d
answered Log normal distribution - Where am I wrong?
1d
comment Log normal distribution - Where am I wrong?
Your second line is incorrect. $X$ has a mixture normal distribution and not a normal distribution as the last equality on the second line asserts. Your calculation of the pdf of $Y$ as a mixture of log-normal distributions is correct; the statement made on line 3 is not.
1d
comment factorisation over a galois field
You began with the given primitive polynomial $x^3+x+1$ and said "Let $\alpha$ denote a root of this polynomial" from which you got the table. Note that you used this polynomial to determine that $\alpha^3 = \alpha+1$ etc. So now you are working out $(x-\alpha)(x-\alpha^2)(x-\alpha^4)$ which is a polynomial that has $\alpha$ as a root, and also has all the conjugates of $\alpha$ as roots. So you know, I hope, that this polynomial must have coefficients in $\mathbb F_2$ and also that the polynomial must be divisible by the minimal polynomial of $\alpha$.
1d
answered factorisation over a galois field
2d
comment factorisation over a galois field
Try reading this detailed answer by Jyrki Lahtonen and see if it resolves the questions you have.
2d
comment Conditional Probability with Normal Distributions
You need to say something about the joint density of $A,B, C$. Are they given to be independent? jointlu normal? etc.
2d
comment What is the mean and variance of $Y$, where $Y$ is sum of iid's
Please delete the $a$ in your last displayed equation, or insert an $a$ on the right hand side.
Aug
27
comment What is the mean and variance of $Y$, where $Y$ is sum of iid's
Is $T_n$, the sum of the $Y_i$, given by $\sum_{i=1}^n Y_i$ or $\sum_{i=1}^n Y_i^2$?
Aug
26
comment Proving that number of codes with even weight is the same as number of codes with odd weight for a specific code book
Hint: The sum of two binary words of even Hamming weight is a word of even Hamming weight. So, the subset of even-weight codewords in a linear code is a subcode. Now show that the odd-weight codewords are a coset of this subcode.
Aug
25
comment Probability in Medical Testing
Real life question?
Aug
22
comment Geometric interpretation of an integral inequality
Your last sentence is incorrect: you want to arrive at $a = E[X]$, not at $a = E[X^2]$. More simply, $$\begin{align}E[(X-1)^2]&=E[((X-\mu) + (\mu-a))^2]\\&= E[(X-\mu)^2] + (\mu-a)^2 + 2(\mu-a)E[X-\mu]\\&= E[(X-\mu)^2] + (\mu-a)^2\\&=\sigma^2 + (\mu-a)^2\\&\geq \sigma^2\end{align}$$ with equality when $a = \mu = E[X]$.
Aug
20
comment Problem solving: Counting and probability
Perhaps $P_{4,20} = 20\times 19\times 18\times 17$ is what you meant to write?
Aug
19
answered Finding the expected value of a function of random variables
Aug
19
comment linear time-constant causal system
Please consider asking the moderators to move this question to dsp.SE where it is a more natural fit. You can contact the moderators by clicking on the flag link below your post.
Aug
19
comment Poisson, Gamma distribution example.
The answers that you seek are given in the problem statement itself: the time of the second arrival has a Gamma distribution with parameters $(2,\lambda^{-1})$. Do you need an explanation of the R code? If so, that is off-topic for this site.
Aug
19
answered why Turbo Code encoder doesn't work if the component codes are recursive but not SYSTEMATIC?
Aug
18
answered what is the meaning behind this combinatorial identity