Math Is Fun Forum

Given a random variable X with probability density f(x) = x/8 for 0 ≤ x ≤ 4:
1) What is the probability that X is between 1 and 3?
2) Find the expected value of X

How do you find the expected value for these type of questions? In general to find the expected value you use (x*(p(x)), so does that mean you have to plug in numbers 0 to 4 and apply the same formula after? Also for number 1 I got 1/2 as an answer.

Hi, I am a little confused about this problem:

An urn contains four balls numbered 1,2,3 and 4. If two balls are drawn from the urn at random (that is, each pair has the same chance if being selected) and Z is the sum of the numbers on the two balls drawn, find:

a) the probability distribution of Z

What I got for the answer was:

Urn= {1,2,3,4}
Z= {3,4,5,6,7}

p(3) = 1/4        //(1 way to get 3)
p(4) = 1/4       //(1 way to get 4)
p(5) = 1/2       //(2 ways to get 5)
p(6) = 1/4      //(1 way to get 6)
p(7) = 1/4      //(1 way to get 7)

Is this was the question was asking for? I wasn't quite sure. Though I think my answer is wrong because aren't they supposed to add up to 1?

I'm having a hard time of understanding the meaning of those two and am also confused about which formula to use when given a problem related to those methods. What does it mean when it say things like "Order does not matter," or "No replacement"?

When should I use the comparison test? What indications should I look out for?

∫ dx/(x^2 + 9)

The answer to that is 1/3 arctan (x/3) + C, but what are the steps to getting there? Where does the x/3 come from when using U-substitution (u = x/3)?

Hi, I'm confused about how to convert something like (0,2) to Polar coordinates. The correct formula is this right?:

r^2= (x^2 + y^2)^1/2
Θ = tan^-1 (y/x)

When I plug in the values, I'd get something like Θ = tan^-1 (2/0). How would you continue in a situation like this? Am I doing something wrong?

Hi, I'm really confuse about how to set up the integral to find the volume. Why did they set up 2 integrals and add them together for the disc method? Also how do you go about choosing the correct values to use? I never understood that.

The graph and answer looks like this (sorry, didn't know how to type it with a keyboard):
i.imgur.com/ob4XQ.png

The question is:

The region in the first quadrant bounded by x=y^2, y=0 and x+y=2 is revolved about the x-axis.
a) Set up an integral(or integrals) to evaluate the resulting volume using the disc method. (Set up only)
b) Do the same problem using the shell method. (Set up only)