Finding a probability of variable's 1st and/or 2nd digit being 3 from uniform distrb.

[cathex]

Hi,

Problem 1:

A random variable X is uniform [0,1]. Find the probability that X's 2nd digit is 3.

As far as I understood, I need to find the probability of interval 0.03 - 0.04? And also all intervals that have 3 in 2nd digit? Like:

0.03 - 0.04
0.13 - 0.14
0.23 - 0.24
0.33 - 0.34
0.43 - 0.44
0.53 - 0.64
0.63 - 0.64
0.73 - 0.74
0.83 - 0.84
0.93 - 0.94

And then add the probability of each interval? Could someone help me, please?

Problem 2:

A random variable X is uniform [0,3]. Find the probability that X's first and/or second digit is 2.

I actually don't know how to tackle this problem. Could somebody point out what should I do with this? I don't expect to get the straight answer, just to show what I need to do. Somehow ended up being in class with calculus. Many thanks in advance.

 

[Dr.Peterson]

Hi,

Problem 1:

A random variable X is uniform [0,1]. Find the probability that X's 2nd digit is 3.

As far as I understood, I need to find the probability of interval 0.03 - 0.04? And also all intervals that have 3 in 2nd digit? Like:

0.03 - 0.04
0.13 - 0.14
0.23 - 0.24
0.33 - 0.34
0.43 - 0.44
0.53 - 0.64
0.63 - 0.64
0.73 - 0.74
0.83 - 0.84
0.93 - 0.94

And then add the probability of each interval? Could someone help me, please?

Problem 2:

A random variable X is uniform [0,3]. Find the probability that X's first and/or second digit is 2.

I actually don't know how to tackle this problem. Could somebody point out what should I do with this? I don't expect to get the straight answer, just to show what I need to do. Somehow ended up being in class with calculus. Many thanks in advance.

What do you get for the probability of each interval?

Answering the first question may help you be more confident on the second.

No calculus is actually needed here; but if you are saying that this class requires calculus, and you have no knowledge of it at all, then you should talk to your instructor about whether you should drop the course or whether the calculus needed is basic enough that you can learn it "just-in-time" while you move on.

 

[cathex]

What do you get for the probability of each interval?

Answering the first question may help you be more confident on the second.

No calculus is actually needed here; but if you are saying that this class requires calculus, and you have no knowledge of it at all, then you should talk to your instructor about whether you should drop the course or whether the calculus needed is basic enough that you can learn it "just-in-time" while you move on.

Hey, thanks for the reply. I wish I could stop the course but at this point it isn't possible anymore, so I have to work my way through all the problems. Is it probability theory then, if not calculus? Could you point out the area I should look into? Thanks.

 

[Dr.Peterson]

Hey, thanks for the reply. I wish I could stop the course but at this point it isn't possible anymore, so I have to work my way through all the problems. Is it probability theory then, if not calculus? Could you point out the area I should look into? Thanks.

You didn't answer my question about the probability of each interval. I need to know at least what you were taught about it, in order to help you from wherever you are to where you need to be. It's clear from the work you showed that you do have some understanding of what you need to do; I need to be more sure where the edge of your understanding is.

But "the area you should look into" is, humorously enough, area. The probability that X is in a given interval is the area under the PDF above the given interval; in terms of calculus, that's called an integral, but for this problem you don't need that concept. Here, it's just the area of a rectangle.

Can you show me what you were taught about the uniform distribution, and perhaps an example of finding such a probability? Part of my goal is to help you be able at least to read your textbook, so I need to see at what level it is written, and whether things are stated in a way you can be expected to interpret. (If you tell us its name and author, we may even be able to find it and give you more specific advice.)

I said that you should talk to your instructor, and that is true regardless of what you plan to do. He or she needs to know your limitations, and then may be able to suggest a way to learn whatever calculus you need as you go. There may even be some resources available that are intended for just your situation.

But, frankly, if they let you in the course without the prerequisites, then it is at least partly, perhaps wholly, their fault, and they owe you something.