Hi,
I cant understand about the continuous random var and its range. It says that measurable values are called continuous values. For example length, and time are continuous variables, why? For instance time is 4s why its a continuous var. Why we need a range for saying that time is 4s. Same is true with height. Why range is necessary fro height?

Please guide me.

Zulfi.

 

Hi,
Kindly read the 'range' as 'interval' because Range is associated with all measurable quantities.Sorry about that.

Zulfi.

 

Because time and height are not exact quantities. When you measure your height and claim it could take on any value within a continuous range. You might say that it is 70 inches, but it almost certainly is not exactly 70 inches. It could really be 70.10849328547378567267666365056 inches or 69.9371367506730129 inches.

 

Another way of looking at it is that the probability that your height is any one specific value is infinitesimally small. If you say that you are 70 inches then I would be willing to bet you my entire life savings that you are wrong. Instead, we have to talk about the probability that your height lies somewhere within some interval. So we might say that there is a 90% probability that your height lies between 69.5" and 70.5" or a 99.99% probability that it is between 69" and 71" or a 10% probability that it is between 69.9" and 70.1".

 

Another way of looking at it is that the probability that your height is any one specific value is infinitesimally small. If you say that you are 70 inches then I would be willing to bet you my entire life savings that you are wrong. Instead, we have to talk about the probability that your height lies somewhere within some interval. So we might say that there is a 90% probability that your height lies between 69.5" and 70.5" or a 99.99% probability that it is between 69" and 71" or a 10% probability that it is between 69.9" and 70.1".

So there is a + - error in our measurements and to incorporate that error we say that continuous variables are associated with an interval.

Zulfi.

 

So there is a + - error in our measurements and to incorporate that error we say that continuous variables are associated with an interval.

Zulfi.

That's a big aspect of it, but even without measurement errors, a random variable that represents a measurable quantity can take on ANY value for that quantity.

 

That's a big aspect of it, but even without measurement errors, a random variable that represents a measurable quantity can take on ANY value for that quantity.

==
Hi,
But the probability of continuous variable is zero.

Zulfi.

 

==
Hi,
But the probability of continuous variable is zero.

Zulfi.

The probability of it taking on a specific value is infinitesimally small -- I've already stated that. Consider that you know that the length of an object is about midway between 1.2 m and 1.3 m. You know that it actually is one specific length (at least at any moment in time), but no matter how tightly you narrow down the limits, there are an infinite number of lengths that it could be within that interval, so the odds that it is any particular one of them approaches zero. For instance, what is the likelihood that the length is exactly 1.2498002911382741934822198301933759371? You could safely bet your entire life's savings that it is NOT exactly that length and feel very confident in your bet, right?