Ben Chuanlong Du's Blog

And let it direct your passion with reason.

Inverse of a Special Class of Matrices with High Dimensions

One day, my officemate Tieming asked me about a problem that she met in her research. Suppose \(\boldsymbol{B}\) is a symmetric matrix of huge dimension and \(\boldsymbol{D}\) is a diagonal matrix with nonnegative diagonal elements. The inverse of \(\boldsymbol{B}\) is already known, how can we calculate the …

Which One Is the Best Strategy? (continued)

Suppose we flip a coin which has probability 0.7 to be head again and again and two people choose two different sequences of length 3 (e.g., THH). The people whose sequence appears first wins. If you are allowed to choose first, which sequence will you choose?

I discussed …

Expected Gain of Tossing a Dice

Suppose you toss a symmetric dice. You are allowed to quit the game and get money which equals the total points you get at any time if 6 has never showed up. Whenever 6 shows up, the game is over and you get nothing. For example, if the first three …

Randomly Select an Integer?!

I found this "probability" problem when I read a person's blog.

What's probability that two randomly chosen nature numbers are relatively prime?

It is claimed that there is a very elegant solution for this problem. This problem reminds me another one. Some people asked for an example of a 0-probability …

Fix Microphone Problem of Skype in Debian

Install Pulseaudio if you only have ALSA. ALSA alone does NOT work with skype whatever people on the #Debian channel might think and tell you.

sudo apt-get install pulseaudio

Install pulseaudio volume control

sudo apt-get install pavucontrol

Run Skype.

Go to the Sound devices sections. Click on the Open PulseAudio …

Culture of My Summer Intern Team

I work as a student intern in the Credit Portfolio Risk Analysis group in a bank this summer. One Friday afternoon, Jimmy, the manager of my manager, asked me to his office and talked about our team cultures.

  1. Ownership
    Whenever you have a project, you are the ownner. Be proud …