# Continuous random Var range and example

Gold Member

## Homework Statement

Why we use range with continuous random and why is time continuous var and why we associate a range with it?

Theoreticl topic

## The Attempt at a Solution

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?

Zulfi.

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Stephen Tashi
With time, you can have 4s, 4.1s, 4.15s. By contrast with "number of children in my family", you can have 4 or 5 but not 4.1 or 4.15.

Mark44
Mentor

## Homework Statement

Why we use range with continuous random and why is time continuous var and why we associate a range with it?

Theoreticl topic

## The Attempt at a Solution

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?
The answer is farily simple. A continuous random variable can take on any real value within an interval, while a discrete random variable can take on only integral values within some range. Measurements of length, time, weight, and so on are continuous, but counts are discrete.

An item could weigh 6.32 lb., for example, but the number of successful outcomes of some kind wouldn't be 6.32.

Gold Member
Hi,
<

With time, you can have 4s, 4.1s, 4.15s. By contrast with "number of children in my family", you can have 4 or 5 but not 4.1 or 4.15.
>
Thanks Stephen. I cant understand why range is necessary for continuous var.

Zulfi

Ray Vickson
Homework Helper
Dearly Missed
Hi,
<

With time, you can have 4s, 4.1s, 4.15s. By contrast with "number of children in my family", you can have 4 or 5 but not 4.1 or 4.15.
>
Thanks Stephen. I cant understand why range is necessary for continuous var.

Zulfi
Continuous random variables need not have a finite range. For example a normally-distributed random variable can go from near $-\infty$ to near $+\infty$, but very large positive or negative values are extremely improbable. For example, an event with a probability of $p =10^{-1000000000000000}$ is so unlikely that you could safely say you would likely never observe it in our universe. Nevertheless, $p \neq 0.$

Stephen Tashi
Why we need a range for saying that time is 4s. Same is true with height. Why range is necessary fro height?
It isn't a situation of having a range or not having a range. All measured quantities "have a range". For example, the number of children in a family has a range consisting of 0,1,2,... The number of children in a family is not a continuous random variable, but it does have a range.

Gold Member
Hi,
Thanks Ray Vickson, I am able to understand why the probability can be zero for continuous random variables for t= 7.1234s
By for t= 4s will the probability be again zero?

Thanks Stephen Tashi, I am able to understand the concept of range. Now I want to know why an interval is necessary for continuous random variable?

They are defined over an interval of values
Thanks for clearing my concepts.

Zulfi.

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

Why we use range with continuous random and why is time continuous var and why we associate a range with it?
...

Zulfi.
Hi Zulfi,

What is the context of your question ?

Gold Member
Hi,
Continuous Random Variables in the context of Probability

Zulfi.

Ray Vickson
Homework Helper
Dearly Missed
Hi,
Thanks Ray Vickson, I am able to understand why the probability can be zero for continuous random variables for t= 7.1234s
By for t= 4s will the probability be again zero?

Thanks Stephen Tashi, I am able to understand the concept of range. Now I want to know why an interval is necessary for continuous random variable?

Thanks for clearing my concepts.

Zulfi.
Purely continuous random variables have the property that any particular value has probability zero. Thus, for a continuous random time $T$ the event $\{T = 7.123 \; s \}$ has probability zero and so does $\{ T = 4 \; s\}.$ Nevertheless, whenever we "observe" $T$ we do get some particular value! That type of concept can be hard to grasp, so don't be discouraged if you are having trouble understanding it. (Exactly the same type of thing occurs in Physics when we speak of m"mass density" or ""charge density", etc.)

In fact, whenever you measure something like a time or a weight or a length, you are always getting a value with some unknown built-in error. So, when we say that $T = 7.233\; s$ we likely mean $T \in (7.2329, 7.2331)$ or something similar. Intervals like that can have positive probabilities, not zero. To account for that we define a concept called density (in this case, density of probability or probability density) so that we have a way of comparing such interval probabilities at different "base" values of $t$. In other words, for small $\Delta t > 0$ we have
$$P\displaystyle \{ t - \frac{1}{2} \Delta t < T < t + \frac{1}{2} \Delta t \} = f( t) \Delta t$$
for very small $\Delta t.$ That way we can assess whether $T$ is likely to be near 1 or near 2 or near 10 or ... .

Last edited:
Gold Member
Hi,
Thanks Ray Vickson. Built in Error logic is possible.
Why in post#5 you said probability is not zero.
Zulfi.

Ray Vickson