Question

In the interval [0,1]
\(A=\{x|0\leq x\leq1/3\}\)
\(B=\{x|1/3\leq x\leq1\}\)
\(C=\{x|x=1/3\}\)
\(A=\{x|1/2,x,5\}\)
Use your intuition to assign values to
P(A),P(B),P(C),P(D)
Please, help

Answer 1

gotta use my intuition to read it !

Answer 2

I'm not sure but I'm hoping this link will be able to help you: https://github.com/juergenmeinecke/EMET1001/blob/master/sets.rst

Answer 3

i assume there is something more to this question
a point is chosen uniformly on \([0,1]\) for example and
\[A=\{x|x\leq \frac{1}{3}\}\] then
\[P(A)=\frac{1}{3}\] the length of the interval

Answer 4

The net's fault, not mine, hihi

Answer 5

@satellite73 I got you, but how to find P(C)??

Answer 6

Sorry is this probability or real analysis?

Answer 7

The tittle of book is" Probability and Statistical Inference" by Hogg, Tanis and Zimmerman

Answer 8

Oh okay. You're given the uniform distribution (which is continuous). The probability of the random variable attaining a point in a continuous distribution is zero.

Answer 9

You mean P(C) =0??

Answer 10

Yes

Answer 11

And P(D) =1/2, right?

Answer 12

Correct, the \((1,5)\) part of the interval is zero, so you're left with 1/2.

Answer 13

P(A) = 1/3 , P(B) = 2/3 , P(C) = 0 , P(D) = ?

Answer 14

Thank you so much.
One more question, I don't see the definition of " probability of the random variable attaining a point ... is zero", on my book. Can you give me link?

Answer 15

can you define D again? D = 1/2 <= x <= 5 ?

Answer 16

since the universal set here is [0,1] , then it would just be 1/2

Answer 17

D ={ x | 1/2<x<5}

Answer 18

yes, that is my answer too. In the given interval, it is (1/2,1)

Answer 19

Think of it this way.
\[P(c)=P(c\le X\le c)=\int_c^cf(x)~dx=0\]

Answer 20

Got you. :)

Answer 21

Thanks again.

Answer 22

you can think of it, each point has the same probability of being picked . and there are an infinite number of points between 0 and 1 . so the probability of picking any specific point in [0,1] is going to 1 / infinity or zero

Answer 23

You're welcome!

Answer 24

Thanks @perl too. I learn a lot :)

Answer 25

what is interesting is that any number you pick has a probability of zero to occur, but you pick a point each time. so saying something has the probability of zero does not mean it is impossible to happen

Answer 26

any number you pick had a probability of 0 of occuring before you picked it, but you do pick a number . so probability of zero does not imply it is impossible to happen

Answer 27

it just means, given that each point between 0 and 1 is equally likely , it is very very very unlikely you pick a specific point like 0.23457899

Answer 28

essentially the probability of picking a decimal that im thinking of between 0 and 1 , im thinking of a number right now, is zero .

Answer 29

so ask someone to pick a number between 0 and 1, and then randomly throw a dart at the line [0,1]

Answer 30

the probability your dart will land on the number your friend picked is zero (but not impossible)

Answer 31

I understood. :)

Answer 32

clearly the dart does land on the line ;)

Answer 33

sorry im pedantic. being pedantic is good when you are first learning a new theory

Answer 34

it will resolve ambiguities later on

Answer 35

questions that may occur

Answer 36

\[P(C)=0\]

Answer 37

the point has no length

Answer 38

No, no. I need seeing the problem from different perspective. Thanks for giving the information.

Answer 39

oh waht @perl said

Answer 40

yup.

Answer 41

is it wrong to steal a medal from a guy who has a lot of gold and give it to a not so wealthy person

Answer 42

by steal, i mean undo giving a medal and give it to someone else

Answer 43

i dont know what this is called, indian giving?