How is Quoted stock prices on the NASDAQ is an example of discrete random variable? Shouldn’t this be continuous? Could you explain this by an example?
sgupta0827 Wrote: ------------------------------------------------------- > How is Quoted stock prices on the NASDAQ is an > example of discrete random variable? Shouldn’t > this be continuous? Could you explain this by an > example? I am not sure but I think it is because they quote the price to 2 decimal places (which of course makes sense) So though there are infinite values, they are still discrete since between any two values there are not infinite values. In the case of continuous, there are infinite values between any two values. Think number line and how there are infinite points between any two points on the number line.
anish Wrote: ------------------------------------------------------- > sgupta0827 Wrote: > -------------------------------------------------- > ----- > > How is Quoted stock prices on the NASDAQ is an > > example of discrete random variable? Shouldn’t > > this be continuous? Could you explain this by > an > > example? > > > I am not sure but I think it is because they quote > the price to 2 decimal places (which of course > makes sense) So though there are infinite values, > they are still discrete since between any two > values there are not infinite values. > In the case of continuous, there are infinite > values between any two values. Think number line > and how there are infinite points between any two > points on the number line. Thanks Anish…That helps!..btw the other choice in the question was “return on real state investment”. I think return will always be continuous. Right?
Return on real estate would be discrete wouldn’t it? There are no range of returns for this.
bar that i understand yeah it is continuous
sgupta0827 Wrote: ------------------------------------------------------- > anish Wrote: > -------------------------------------------------- > ----- > > sgupta0827 Wrote: > > > -------------------------------------------------- > > > ----- > > > How is Quoted stock prices on the NASDAQ is > an > > > example of discrete random variable? > Shouldn’t > > > this be continuous? Could you explain this by > > an > > > example? > > > > > > I am not sure but I think it is because they > quote > > the price to 2 decimal places (which of course > > makes sense) So though there are infinite > values, > > they are still discrete since between any two > > values there are not infinite values. > > In the case of continuous, there are infinite > > values between any two values. Think number > line > > and how there are infinite points between any > two > > points on the number line. > > Thanks Anish…That helps!..btw the other choice in > the question was “return on real state > investment”. I think return will always be > continuous. Right? Ya. Generally speaking, a calculated quantity will be continuous because calculation could give you any value i.e. infinite values between 2 values e.g. between 2 and 3%, you could get return as 2.385674% and 2.444444444…% etc depending on the numbers. The quoted return could be discrete if you round it off to closest values.
anish Wrote: ------------------------------------------------------- > sgupta0827 Wrote: > -------------------------------------------------- > ----- > > anish Wrote: > > > -------------------------------------------------- > > > ----- > > > sgupta0827 Wrote: > > > > > > -------------------------------------------------- > > > > > > ----- > > > > How is Quoted stock prices on the NASDAQ is > > an > > > > example of discrete random variable? > > Shouldn’t > > > > this be continuous? Could you explain this > by > > > an > > > > example? > > > > > > > > > I am not sure but I think it is because they > > quote > > > the price to 2 decimal places (which of > course > > > makes sense) So though there are infinite > > values, > > > they are still discrete since between any two > > > values there are not infinite values. > > > In the case of continuous, there are infinite > > > values between any two values. Think number > > line > > > and how there are infinite points between any > > two > > > points on the number line. > > > > Thanks Anish…That helps!..btw the other choice > in > > the question was “return on real state > > investment”. I think return will always be > > continuous. Right? > > > Ya. Generally speaking, a calculated quantity will > be continuous because calculation could give you > any value i.e. infinite values between 2 values > e.g. between 2 and 3%, you could get return as > 2.385674% and 2.444444444…% etc depending on the > numbers. The quoted return could be discrete if > you round it off to closest values. The only doubt i had is if you could round off the price then why can’t you round off the returns?
The quoted price is not rounded - it’s actually in pennies. If you round a price, it’s still continuous - you merely present it as rounded.
sgupta0827 Wrote: - > The only doubt i had is if you could round off the > price then why can’t you round off the returns? Sure you can. e.g. If you present every return upto 2 decimal places, the data becomes discrete.
Discrete random variable can only take at most countably infinite values. Continuous random variable takes uncountably infinite values. Countable basically means you can list all of the values 1 by 1 in some meaningful way. For the purpose of this exam the random variables will always take on a subset of the real numbers we we can reduce it to. Discrete random variables do not take values according to an interval of the real numbers Continuous random variables take on values according to an interval of real numbers. For example. IF they take on the values (1,2,3,4…infinity) then its discrete But if they take the value “all real numbers between 0 and 2” then its continuous. Saying “A random variable is continuous if it can take infinite values between any numbers” is wrong. Between any two rational number (a/b, where a,b are integers, b not 0). there are infinite rational numbers. I.E. between 1 and 2 there are 1/2, 1/3, 1/4 … 2/3, 3/4 …etc. Clearly there are infinite of them. However the Rational numbers are countable and thus a random variable that can only take rational numbers will be discrete. The fact that the rational numbers are countable is a fairly surprising result that wont come up on the CFA exam. However you can often use continuous distributions on discrete random variables as a good approximation if the ‘distance’ between values the random variable can take are ‘sufficiently small’.