At this moment writing this I just want to remind myself of some pretty interesting problems in probability that I have encountered in the past few days. Without wasting any time let me just begin :
In an independent trials of a fair dice , what is the probability that 1 will show up before 6 ?
There are s urns and n balls (n>s) to be distributed among them. What it the expected value of the variable Y(k) which indicates the number of urns that have exactly k balls ? Its variance ?
What is the expected value of number of flips which is conducted in this manner : I keep on flipping a fair coin until I get two tails ? (Hint: derive it knowing that the expected number of flips that are done before one gets a head is 1)
So there are n nodes that want to send their packets in the next given time slot. Each of them has probability p of transmitting a packet. What is the probability there is a collision ? What is the probability that a packet finds a collision ? (Hint: the two answers are different)
Will update as I find some more !
Saturday, September 25, 2010
Friday, January 29, 2010
The Infanticide of Dreams
Well, it' s been a really long time since I have decided to write something that is on the top of my mind. I must concede that my current job has seriously plundered whatever penning skills I acquired over the years. Though I try to supplement this void with some fiction titles, it is hardly as gratifying as the tiny triumphs that one can get in inditing his views.
So cutting short my sob story, lets jump to the point. Today, after I finished my voluntary teaching at a nearby government school I had this reverberating slogan "Each one, Teach one" running in loops in my head. Not sure whether it was due to the contained smiles of the young kids or the conscience trail in my head that me made to ponder about this depth of this innocuous tiny rime. It is unimaginable how much a tiny effort by each one of us can make a difference to the lives of these young aspiring kids who have been deprived of the basic rights to free opportunities. Yes, it is correct what I just said, they have indeed no equal opportunities when compared to english speaking urban bred children of professionals. I remember once arguing with my socialist friend that the greatest evil in a system is not the divide between the rich and the poor or the monopoly by the plutocrats but the denial to equal opportunity. The society must ensure that each individual must be given an equal chance and no less. So when someone says that one day he wants to lead this country, the words do carry a meaning. Coming back to the school, majority of the kids here spend most of their time doing household chores and the rest of it loitering in the streets. Their lesser educated parents carry on with a belief that sending their kids to school will ensure a better future for them. But tell me how will the 12 yr old Shivaraj who cannot even spell the word 'doctor' will ever achieve his dream of becoming a doctor? He will most likely quit school after he flunks the tenth grade and will occupy the shoes of his ageing father running his paan shop. Tell me what society is this where even dreams become a near perpetual sin ? What has the kid done wrong to deserve a life like this ? The principals of the society come crumbling down in the case of young Shivaraj who is content smiling all through the two hours of the class. So the imminent question is: How do we provide an equal chance for this kid to chase his dream ? How will he ever compete with the scores of english educated rich kids with their fancy science projects and extra curriculars ? No , I am not talking about the intellectual abilities of Shivaraj, never mind if he realises that he was never meant to be a doctor, but we should atleast give him that opportunity to decide. This infanticide of dreams is what I am pointing to. How will he ever know about the Harvard medical school or our own AIIMS which he may hope to join ? Sitting in the shabby classroom, little does Shivaraj know that every passing moment is taking him closer to a life of never ending misery.
So who is responsible for every kid that stays back from school ? Its you, its me and each one of us. All these young souls needs is right guidance, which can let them know that their dreams can be turned into a reality. Is it too much to ask for? So lets make a pledge today that each one of us will teach atleast one of them.
So cutting short my sob story, lets jump to the point. Today, after I finished my voluntary teaching at a nearby government school I had this reverberating slogan "Each one, Teach one" running in loops in my head. Not sure whether it was due to the contained smiles of the young kids or the conscience trail in my head that me made to ponder about this depth of this innocuous tiny rime. It is unimaginable how much a tiny effort by each one of us can make a difference to the lives of these young aspiring kids who have been deprived of the basic rights to free opportunities. Yes, it is correct what I just said, they have indeed no equal opportunities when compared to english speaking urban bred children of professionals. I remember once arguing with my socialist friend that the greatest evil in a system is not the divide between the rich and the poor or the monopoly by the plutocrats but the denial to equal opportunity. The society must ensure that each individual must be given an equal chance and no less. So when someone says that one day he wants to lead this country, the words do carry a meaning. Coming back to the school, majority of the kids here spend most of their time doing household chores and the rest of it loitering in the streets. Their lesser educated parents carry on with a belief that sending their kids to school will ensure a better future for them. But tell me how will the 12 yr old Shivaraj who cannot even spell the word 'doctor' will ever achieve his dream of becoming a doctor? He will most likely quit school after he flunks the tenth grade and will occupy the shoes of his ageing father running his paan shop. Tell me what society is this where even dreams become a near perpetual sin ? What has the kid done wrong to deserve a life like this ? The principals of the society come crumbling down in the case of young Shivaraj who is content smiling all through the two hours of the class. So the imminent question is: How do we provide an equal chance for this kid to chase his dream ? How will he ever compete with the scores of english educated rich kids with their fancy science projects and extra curriculars ? No , I am not talking about the intellectual abilities of Shivaraj, never mind if he realises that he was never meant to be a doctor, but we should atleast give him that opportunity to decide. This infanticide of dreams is what I am pointing to. How will he ever know about the Harvard medical school or our own AIIMS which he may hope to join ? Sitting in the shabby classroom, little does Shivaraj know that every passing moment is taking him closer to a life of never ending misery.
So who is responsible for every kid that stays back from school ? Its you, its me and each one of us. All these young souls needs is right guidance, which can let them know that their dreams can be turned into a reality. Is it too much to ask for? So lets make a pledge today that each one of us will teach atleast one of them.
Friday, February 6, 2009
Hallelujah..... its recession
I have never seen a recession in my short life span and I don't know how to be a part of it. The other day I was purchasing bunch of grapes from a roadside vendor when its price struck me. Guess what ... the price is same as it was 10 months ago or perhaps a year ago. Now with the hoo-hah about the recession in the backdrop of our lives and the much caused pain caused by it, I was left wondering if I am being taken for a ride for my princely appetite. Well if there is a so called liquidity crunch and a demand destruction present in the economy, then why isn't the shrewd vendor giving me any concessions ?? For I must be among the few number of customers paying a visit to his base. Why is he so inflexible in his pricing ? Why isn't the ugly head of recession showing up when he arrogantly snubs down my attempt for a haggle? It seems his ego goes hand in hand with the price.
Well let me break down my experience in terms of a paradoxical market phenomenon that is building up in the aftermath of the worst economic crisis ever.
Consider the situation a year ago when the economy was hale and hearty and the prices were reaching the skies. The demand outran the supply by a huge amount and the prices followed a non linear path. Retailers, vendors, autowallahs, even the local nescafe had upped the prices forseeing an increased demand. In some cases the hike was an unjustified 50% (Icetea costing Rs 15 from a previous Rs 10). The double digit inflation seemed to justify this and with record levels of production and spending the hike was all very well cushioned. All the figures, IIP, FDI ... etc were at an unprecedented green levels. Even the stock indices zoomed to staggering levels. Everyone hoped to cash on this and made astonishing irrational decisions of raising prices, adding human resources, expanding and piling up debt that was way beyond their limits. But then the catastrophe struck that only their grandfathers would know about.
As the story goes, money dried up in the market and the blood bath ensued. However, the prices remained inelastic. The reality prices did not scuttle nor did the price of icetea and not even the grapes. So what happens when the demand cannot keep up with the price ?
Simple .... blood gets spilled. Look at the reality stocks off late, they were trading at a lifetime high (DLF ~ Rs 1200) then and now they are flooring at record lows (DLF ~ Rs 150).
And what about the domestic airlines that refused to pass reduction in surcharges to the customers, they mounted enormous losses. However, my friend at the fruit stall does not know much about this and continues pricing at levels that would no longer be sane. Yes, this is the tendency of people, the inertia of a system that remains inelastic to changes. Owners and residents would never sell a flat at 15 Lacs that was priced at 35 Lacs the very last year. The nescafe would never revert back to the previous rates.
So here lies the greatest catch. It would be the burst of people's ego before any other economic bubble bursts. The revenues will crash and so will the brand. Demand will be lost and profits would be thrashed. Vendors and retailers would be slapped and kicked to respect the market and made to realize that it is the consumer like me who rules the roost in a capitalistic society.
Please leave a comment.
Well let me break down my experience in terms of a paradoxical market phenomenon that is building up in the aftermath of the worst economic crisis ever.
Consider the situation a year ago when the economy was hale and hearty and the prices were reaching the skies. The demand outran the supply by a huge amount and the prices followed a non linear path. Retailers, vendors, autowallahs, even the local nescafe had upped the prices forseeing an increased demand. In some cases the hike was an unjustified 50% (Icetea costing Rs 15 from a previous Rs 10). The double digit inflation seemed to justify this and with record levels of production and spending the hike was all very well cushioned. All the figures, IIP, FDI ... etc were at an unprecedented green levels. Even the stock indices zoomed to staggering levels. Everyone hoped to cash on this and made astonishing irrational decisions of raising prices, adding human resources, expanding and piling up debt that was way beyond their limits. But then the catastrophe struck that only their grandfathers would know about.
As the story goes, money dried up in the market and the blood bath ensued. However, the prices remained inelastic. The reality prices did not scuttle nor did the price of icetea and not even the grapes. So what happens when the demand cannot keep up with the price ?
Simple .... blood gets spilled. Look at the reality stocks off late, they were trading at a lifetime high (DLF ~ Rs 1200) then and now they are flooring at record lows (DLF ~ Rs 150).
And what about the domestic airlines that refused to pass reduction in surcharges to the customers, they mounted enormous losses. However, my friend at the fruit stall does not know much about this and continues pricing at levels that would no longer be sane. Yes, this is the tendency of people, the inertia of a system that remains inelastic to changes. Owners and residents would never sell a flat at 15 Lacs that was priced at 35 Lacs the very last year. The nescafe would never revert back to the previous rates.
So here lies the greatest catch. It would be the burst of people's ego before any other economic bubble bursts. The revenues will crash and so will the brand. Demand will be lost and profits would be thrashed. Vendors and retailers would be slapped and kicked to respect the market and made to realize that it is the consumer like me who rules the roost in a capitalistic society.
Please leave a comment.
Sunday, January 20, 2008
Why squander money for inattention?
Being my first post on this series, I would straight away bring out my views about an issue that has persistently
been bothering me and more so whenever I happen to be around any gas or petrol station. Why do these Oil Majors like IOC, BP,HP, Reliance.... have to simply spend so extravagantly on their advertisement and brand building ?? Turn on your TV and you invariably end up noticing the big shot celebs endorsing these commodities and talking gibberish with whatsoever no logical relationship to the products and you end up secretly chanting to yourself, praying for the advertisement to run out life! Be it at the billboards or at the humongous boards atop flyovers and highways, in the well lit luminous spof its ace of ten storey buildings or as a moving sticker on your favorite webpage .... they do raise some eyebrows but anyone sober enough is quick to dismiss it. Yes we do savor the appearances of our celebrities, be it Dhoni, Pathan, Sani mirza or any one else but then they completely steal away the show. Hardly can we recall who of them had been an ambassador for HP?
been bothering me and more so whenever I happen to be around any gas or petrol station. Why do these Oil Majors like IOC, BP,HP, Reliance.... have to simply spend so extravagantly on their advertisement and brand building ?? Turn on your TV and you invariably end up noticing the big shot celebs endorsing these commodities and talking gibberish with whatsoever no logical relationship to the products and you end up secretly chanting to yourself, praying for the advertisement to run out life! Be it at the billboards or at the humongous boards atop flyovers and highways, in the well lit luminous spof its ace of ten storey buildings or as a moving sticker on your favorite webpage .... they do raise some eyebrows but anyone sober enough is quick to dismiss it. Yes we do savor the appearances of our celebrities, be it Dhoni, Pathan, Sani mirza or any one else but then they completely steal away the show. Hardly can we recall who of them had been an ambassador for HP?
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