We first identify the study population (say, all iPhone 4′s in Canada) and parameters for attributes we are interested in (we will need θ to be the proportion of these iPhone 4′s which are faulty/defective pieces of lemonware—in other words, the chance that you will receive a catastrophic failure of an iPhone).

We start by assuming that the parameter θ has a certain reasonable value (like 0.001, which says, on average, we think 1 in 1000 iPhone 4′s are defective in the study population). You should note that any numbers here are just guesses I’m making for illustration’s sake. Nowhere am I claiming these values or figures are real or confirmed or even remotely representative of the actual failure rates. Don’t sue me, Apple. Your legal expenses will be greater than everything you’d get bankrupting me.

Anyway, say this is the case. Then let the random variable Y be “we get a working iPhone 4 on the k^th iPhone” where k = 1, 2, … (all positive integers). So then, the probability of the random variable Y taking on the realization of the plain integer y would be:

P (Y = k) = θ ^{k – 1} (1 – θ)

You may recognize this as the geometric distribution and indeed it is. What we are saying is, there will be (k – 1) catastrophic failures before the k^th iPhone is one that works. We also assume you’d stop driving all the way to the Apple Store to ask for and pick up replacements once you get a working one. I think this model is fair, as long as you stop replacing them eventually.

For example, if the first iPhone you get is fine, then k = 1 and we are done. The probability of this is P(Y = 1) = (1 – θ) (since θ to the power of 0 equals 1). Substituting the hypothesized value of θ in, you’d get that the chance of you getting a working iPhone 4 on the first try would be something like 999/1,000 or 99.9%.

Say your first one is a dud, but the replacement works out to be perfect. Then:

P(Y = 2) = (1/1,000)(999/1,000) << (the chance of a lemon) x (the chance of not a lemon)

= 999/1,000,000

= 0.000999

= 0.0999%

However, if you are me, then let k be greater than 2.

P(Y = k) = P(Y > 2) << strictly greater than 2

= 1 – [P(Y = 1) + P(Y = 2)] << this is the probability of everything (1) minus the prob’s of k = 1 and k = 2

= 1 – [999/1,000 + (1/1,000)(999/1,000)] << calculated above to be 0.999 + 0.000999

= 0.000001 << this is 1 in 1,000,000 if you don’t realize

That’s right folks. If the 1:1,000 failure rate is anywhere close to reality (and I’m not saying it is) then what I’ve gone through so far is one in a million. Of course, if the real rate is closer to 1% then it’d be like one in ten thousand, which is still really unlikely, though scaled back a bit.

Basically, the first iPhone 4 I received (after ordering on launch day and waiting three weeks for it to ship—nevermind the mishap where FedEx sent my iPhone to me, then to Vancouver, before sending it back to me) turned out to have a busted compass (GPS sensor was broken) and a busted gyroscope (a new sensor in the iPhone 4). I went to the Apple Store at Fairview yesterday to get it replaced—they didn’t have any stock so they had to order a replacement unit for me. I was told it would take three to five days to get there, but it arrived by 9 pm the same night. So, like a good boy, I drove down to the store again today to pick up the replacement. Just my luck: the replacement was another lemon! iTunes could not detect/connect to the replacement phone. Seriously. Two in a row, both lemons, when this phone is supposed to be of something really special/high-calibre.

Sidenote: you’d think someone at Apple would’ve thought of “let’s check these replacement units before they leave the door because it might make us look completely stupid if we replaced a lemon with another lemon”, but no. I can’t explain why (ask Apple, they might have a coherent reason, but I can’t think of any).

If I ever do get a working iPhone 4, it’ll be in the case where k > 2. If the next one works (i.e. the third one), then I think the probability of that (being a subset of k > 2) is something in the range of  0.000000999, or 9.99*10^-9 if we stick with the 1 in 1,000 assumption.

Anyway, fired off an email to Steve Jobs and I wonder if he’ll ever respond. I asked him to put a few of his engineers on the task of figuring out the exact probability of getting my package incorrectly sorted by FedEx, having two sensors arrive as broken in the same iPhone, and then getting a lemon replacement unit that can’t be detected by iTunes. I added a bonus question for them to predict the probability that my next replacement unit would actually work as advertised.

It wasn’t all sarcastic though—I did mention the fact that I’ve often stood up for Apple’s philosophy of making high-quality stuff that’s worth the extra money, provided it works, but the bullshit attitude of the “Genius” girl at the Fairview Apple Store today and the impotent store manager (who could only offer apologies and “explanations” like “Well as you can see there’s nothing I can do about anything ever”) really made a sizeable dent in my opinion of Apple. Sure there’s nothing you can do, but how about taking my suggestion of “check the replacements before they are shipped out, before you call me, and before I drive down here” seriously, rather than rolling eyes?

Anyway, back to the math: either I really am lucky enough to win the inverse lottery 5+ times (FedEx shipping, attenuation not fixed, Sensor 1, Sensor 2, Lemon Replacement, and probably something else to come)—I was fortunate enough to have, in my one experience, observed something unbelievably unlikely—or the failure rate for these components is actually a lot higher, making these kinds of problems a lot more common than Apple would like. Surely, it must cost more to be playing these cat and mouse games with replacement units than to just employ better quality controls. Then again, it costs Apple next to nothing when I’m the one taking time out of my day and gas out of my car (or bus tokens out of my pocket) to pick up hardware replacements (or in my case, get head-faked again).

Hopefully I get a response from Steve Jobs and I can post the results here. What I really want to see is some sort of “I will look into it” from him. I still love Apple’s stuff, I just really hate my luck and MAYBE I’m starting to hate their quality (controls) and hardware replacement process.

PS: To the “Genius” girl working at the Apple Store rolling your eyes when I mentioned “You can’t keep my signed replacement receipt if this phone doesn’t work, by the way”, FFFFFFFFFFUUUUUUUU.

• watched Audrey Hepburn’s “Charade” with Amy
• got Ulrich the iPhone 4 set up with Fido through a nice Québecois lady, and ended my stay with Koodo
• went to IKEA looking for a bed frame, left with a can opener and a potato peeler
• checked out Buskerfest with Amy (Friday), and then with Adwin and Shawn (Saturday)
• Distillery District for coffees and gelato with Amy

• Matthew Good Band – Indestructible
• Death Cab For Cutie – Marching Bands of Manhattan
• Thousand Foot Krutch – Phenomenon
• Tomoyasu Hotei – Battle Without Honor or Humanity
• Pilate – Into Your Hideout

There’s something wonderful about listening to tracks of a former life that brings back all those memories subconsciously, binding perceptions and recollections the past with the very real and current present.

[ Please visit the original page to listen ]

Died in a motor crash.
I came back for you,
The perfect version of myself.
Tomorrow we start again.
Tomorrow came and went.

I’m indestructible, how?
I’m indestructible.
I’m indestructible, how?
I’m into you. I’m in two.

I’m indestructible.
- Matthew Good Band, Indestructible

Soon, soon my lovely little periwinkles, I will be free of this.

5 things I still want to do before summer ends:

• rock out with Adwin and Stephen (and Melissa too, I guess, but she’s a girl so she doesn’t count)
• head down to Burrito Boyz for lunch with the 1990 guys and back to Rafael’s place for gaming
• find a way to play “Wings of Liberty” Starcraft 2 campaign on Mac or PC
• go on a variety of dates
• see a yet-to-be determined concert

Oh yeah, Linear Optimization. Time to get back on that before day dreaming of dates and video games.

• Statistics on August 3rd
• Business Law on August 5th
• Linear Optimization on August 12th

All in all, this has been a breezy summer term for me. That’s not to say that the courses have all been easy,  I’ve just been going at them as if they were. I should probably be spending all of the coming week reviewing for Stats and Law, and then spending the week leading up to Linear Optimization on that… But, there is Disgaea 3 and my Hi-Capa to play with, so I don’t know how well this will work out.

Note: Managerial Accounting, my fourth course, has no final exam this term. In its place is a group case presentation, and a report due on the same case. Not only am I only responsible for four courses this term, but only three final exams! Win.

• Disgaea 3: Absence of Justice (PS3)
• Tokyo Marui Hi-Capa 5.1 (still needing a name for her)
• Ridge Racer 7 (PS3)
• Battlefield: Bad Company 2 (PS3)
• Syncing “Avatar: The Last Airbender” (cartoon) with Amy

Now back to the distractions!