Making US based NTSC Television work in India

I recently got a US make Samsung HD-LED television. In India we have PAL signal while in US they use NTSC signal. Both the signals are not compatible and as a result, your new TV may not display accurate colors. Here is how to make it work in India:

1. Do not panic in the beginning. If you receive a black and white or distorted display, do not panic. Chances are highly unlikely that you have received a faulty television. So be patient and do a lil bit of study
   
   
2. Check the voltage rating of your TV. Most TVs these days support 100-240V connection. Just to be on a safer side read the manual. In case your manual suggests a 100-110V input then get a power down transformer. Get it from a reputed company or your TV may go woof! Be sure to check the power rating of your TV. What I mean is, check the power consumption. If consumption is 50W then get a transformer of power rating 100W and NOT LESS. Getting a higher power rated step-down voltage transformer should be  your first step
   
   
3. If the display is black and white, you have two options:
   
•  Get a PAL to NTSC converter. There are plenty of these converters starting from 2,000 Rs to 30,000 Rs. It depends on how much you want to spend on these converters. I did some research on Rs 2,000 Mini NTSC - PAL converter. The link is: here. The problem is, I could not find any reviews on the product from India and the ones available on amazon.com are not good. Another downside is the quality. It cannot convert to hi-def standards. So, I decided to chunk this option.
  
• This second option is probably the easier one. I had a NORMAL (not HD) Videocon D2H service in home. So, I decided to drop a facebook message to Videocon's support page. Their response was prompt. A service engineer visited my home the very next day. We came to the conclusion that NORMAL (non HD) Videocon D2H is not compatible with NTSC Signals. However, the engineer advised me to upgrade the service to HD and voila! It works! It only set me back by Rs. 1,400
  

 There are several D2H service providers but not all support NTSC signals in India. I suggest you take a Videocon D2H service (HD) as it is the best and cheapest option for having your US TVs work in India.

Independence and Exclusivity

The concepts of independence and exclusivity of events are intertwined in probability. Often, people get confused between these two concepts. So, the objective of this post is to clarify the difference between the two. Consider two events ${A}$ and ${B}$. The conditional probability of B when A occurs can be written as:

${ P \left( A=a|B=b \right) = \dfrac{ P \left( A = a \cap B = b \right) }{P \left( B = b \right)}}$

Now, let us say when the event $A$ occurs the event $B$ does not occur. For example: let $A$ be the event that it is day now and let $B$ be the event denoting that it is night now. So, can the events $A$ and $B$ ever occur together? The simple answer is no. This means that when event $A$ occurs, the probability of occurring of event $B$ is zero. As a result, both of these events never ever occur together. This means that both these events are exclusive. In simple terms, exclusivity of  two events implies when one of the event occurs, the other event never occurs. So, in the first equation

${P \left( A = a \cap B = b \right) = 0}$

But are these exclusive events independent? Before answering this question, let us first look at what independence of events means. Again, consider two events $C$ and $D$. If these two events are independent, occurrence of one event does not affect the occurrence of the other event. For example consider $C$ and $D$ to be the outcome of a coin toss. Let $C$ denote Heads when you throw the coin once while $D$ denote heads when you throw the coin again. So, you throw the coin once and you get a heads i.e. event $C$ occurs. Does occurrence of event $D$ in any way change? It does not. This means that occurrence of $C$ has in no way altered the chances of occurrence of event $D$. Mathematically, two events are said to be independent if:

${ P \left( A=a|B=b \right) =P \left( A = a \right)}$

Now, let us look at exclusive events and independence together. When the two events are exclusive, it means that one of the events (when it occurs, see the event $A$) alters the chances of occurrence of the other event (see the event $B$, which occurs with zero probability). Therefore, both the events are not independent. Thus, in general exclusivity implies events are not independent. There is another way of look at this problem. Since, we have stated that the events do not occur together, their intersection is zero (cf. second equation). Thus, in the first equation:

${ P \left( A=a|B=b \right) = 0 \neq P \left( A=a \right) }$