Question

https://s17.postimg.org/4qbh651ov/Screen_Shot_2016_11_12_at_6_23_03_PM.png

I don't understand how a density curve is supposed to be able to tell me these things (the answer choices).

Answer 1

@mathmate

I'm always summoning you.

Answer 2

Not sure how to interpret without knowing what each axis represents. In general, if it is called density, the y-axis represents density, but that's a guess. What does the x-axis stand for?

Answer 3

Wait, are those probability density curves?

Answer 4

Let me look

Answer 5

Are you working on probability distributions? Like normal distributions, Poisson, ...

Answer 6

Hm, can you explain what they're trying to say. I don't understand and the link didn't work.

I'm not sure myself, as I'm not sure what they're teaching me. I'll show you two screenshots to help me work through it.

Answer 7

Doesn't you teacher tell you what the subject is before she starts teaching the class? lol

Answer 8

Does your material cover things like tossing a coin, throwing a die, etc (about probability).

Answer 9

This was only labelled density curves.

Answer 10

https://s14.postimg.org/992y8egip/Screen_Shot_2016_11_12_at_7_01_13_PM.png

Answer 11

https://postimg.org/image/glfshuald/

Answer 12

I don't understand how to tell anything about the mean or median though by what they taught me. That was the only page given to us teaching us about density curves so I'm a bit confused.

It's supposed to make a smooth curve and the area under it=1 due to relative frequency histograms but I don't understand their examples.

Answer 13

Any way, I will respond as though they are probability distributions. What gave me the hint was some of the answer options.

To start, in case you do not have a formal presentation on probability distribution, it would be a good idea for you to read up some material, such as
https://en.wikipedia.org/wiki/Probability_distribution
https://onlinecourses.science.psu.edu/stat200/node/34

Next, some properties of a probability distribution are:
1. In general, probability distributions have a domain of -inf to inf. It is custom practice to ignore the domains where the probability is zero. For the case given, we do not know the domain of the distribution, but we do know that the non-zero probabilities are between 0 and 1 (independent variable, domain) , with corresponding probabilities between 0 and 3 (range, or probability).
2. One of the characteristics of a probability distribution is that the total area under the curve is always and exactly 1.0.
3. The median is the value of x (horizontal axis) through which a vertical line will divide the area into two equal parts (of size 0.5).
4. The mean is the integral \(\mu\)=\(\int x p(x)dx\). Geometrically, a vertical line through \(\mu\) passes through the centroid (centre of gravity) of the area.

Answer 14

Ha wow that's a lot of information. While I will, is what was given on that page (that was the only page given to us), not enough for explanation?

Answer 15

@Kikuo
Lol, I was repeating some of the stuff shown on your slides. Yes, the curves represent probability distributions.
I looked at the curves again in a little more detail, they look like parabolas. If not, a parabola would be very close to the curve. So you can use p(x)=3x^2 to verify the median and \(\mu\), but first make sure that the area under the curve is 1.

Answer 16

The second sentence on that page answers directly one of your questions.

I do not know how you would, or could, answer the first question with just the notes given. You will need more information, or more examples to see the relation between mean and median for a curve like y=3x^2 (0<=x<=1). You may want to consult the teacher on that.

However, nothing stops you from using my proposed model to work out some results to attempt answering the first question.

If you have not learned calculus before, it will be difficult for you to answer the first question. :(

Answer 17

I've never learned about parabolas before. We were told we didn't need to know any calculus to do this course. We just needed to know basic arithmetic and beginners algebra.

When I asked my teacher about this lesson she said the probability was taught on that page which is why I was shocked when you gave me all those resources lol.

I was taught the mean is X-bar=E xi/N.

Mean=summation of values divided by number of values in dataset.

I was taught the median is median=N+1/2th term if even and (N/2)th term+(N+1/2)th term/2 if odd

I understand that the area under a density curve that's above the horizontal axis=1.0 since it's based off of relative frequency (which we learned about and understand)

As for the rest I'm confused about since we're supposed to be able to solve the following two questions with everything we've learned on that page without needing to look into additional resources (according to her board).

Answer 18

And without knowing calculus so I'm terribly confused. u.u

Answer 19

What you were taught is good enough to answer questions on a discrete distribution, i.e. each data point is an ordered pair, i.e. P(0)=0, P(1)=3, etc. but P(0.5) is not defined.

That makes a probability mass (not density) function, applicable to things like throwing a die, tossing a coin, etc. What the question gives you is a probability density function applicable to continuous variable, such as the time it takes to wait for a bus, or the volume of beverage filled in a bottle, weight of meat patties in a hamburger, etc. The variable does not count be integers, but by decimal numbers.

Perhaps your teacher expects you to digitize the curve and convert it to a frequency and work with that. This will avoid the use of calculus, but gives an approximation which is good enough to understand the concept.

All in all, I think the instructions and examples are not sufficient to confront you with a question where you have to make assumptions and approximations... but that's life! :(

Answer 20

Alright, let's try to work with that. Give me a minute to re-read what you just said.

Answer 21

Sorry I have to go. If you have any discussion or questions, do post them. I will look at them as soon as I come back in the morning (assuming you're in the same continent!).

Answer 22

Firstly can you explain what the difference is between a discrete and defined distribution is?

We only learned that discrete data is data that's countable and comes as integers where as continuous data has no set number of possibilities (whatever that means).

I will be here.

Answer 23

Actually you explained quite well.
The independent variable (x-axis) of a discrete distribution can only take on integers, such as the number throwing a die, the number of heads when throwing 5 coins, etc.
In a continuous distribution, the independent variable is a decimal number, so there is an infinite number of possible outcomes, 1,1.01, 1.001, 1.0001, 1.0002,1.0003. ....
As I mentioned, some examples are:
the time it takes to wait for a bus, or the volume of beverage filled in a bottle, weight of meat patties in a hamburger, etc.

Answer 24

That is also why a discrete distribution consists of steps while a continuous distribution is (usually) smooth, like the one in your two questions.
You teacher may have skipped at least one page of notes on continuous distributions, or she may have given the wrong example. (sorry no offense to your teacher!)

Answer 25

Luckily we have a book we'll have to read later on that I'm sure will explain some of this.

Alright then, so I understand that now.

Why is a density curve, which is apparently according to my lesson based off of relative frequency, a mathematical model for that distribution?

Can you help me understand the example two picture in the screenshots posted? (If you have time).

Answer 26

The theoretical density curve for the situation of rolling 1 die is a perfectly horizontal line y = 1/6. (Remember this is relative frequency. Confirm that the area under the curve is equal to 1. Since the total area under the "curve" is 1, the area under the curve is a probability.


Why is the density curve for rolling 1 die a perfectly horizontal line which=1/6

Where did they get that number?

It then says confirm the area under is=1. How do we do this?

How do we find the probability based off of that graph they showed us?

Answer 27

A density curve can be thought of as a frequency curve where the independent variable is divided into many, many pieces, so that you almost don't see the steps.