# variable

1. ### Expectation of random variable

Hi, How to prove that $E[X]=\displaystyle\int_0^{\infty}P(X>t)dt$ Answer: $But E[x]=\displaystyle\int_0^\infty xf(x)dx$ How to proceed further? How to arrive at L.H.S.?
2. ### Multiplying square roots

Hey, So this: √(2t^(2)+1+2t)*√(2t^(2)+1+2t) is equal to 2t^(2)+2t+1 But I can't seem to understand how, and what rules... PLS HELP
3. ### Multi variable calculus question

Find the surface area of the surface S. S is the intersection of the plane 3x + 4y + 12z =7 and the cylinder with sides y = 4x^2 and y = 8- 4x^2.
4. ### Cancellation of terms to solve for a variable

My teacher has this problem that I will illustrate below. I could probably solve it the long way, but he uses some unique cancellations to make it easier to digest. There are two things I do not understand about this problem: 1. How is it or why (rather) is it legal to cancel out all of the...
5. ### How do I analyse clinical data that has a variable number of measurements per patient

Thanks in advance for any help you can offer. I'm a PhD student and have just finished recruiting for an observational clinical study. Basically, I have recruited 100 patients and performed imaging of their coronary arteries. The measurements of the coronary arteries (e.g. diameter of vessel...
6. ### 3 Variable System of Equations

Any thoughts on this? Thank you. For a certain value of , the system has no solutions. What is this value of ?
7. ### Change of Variable Formula

Let R be the solid torus in R3 obtained by revolving the circle (y-a)2+z2<=b2 in the yz-plane about the z-axis. Note that the mapping T defined by x=(a+wcosv)cosu, y=(a+wcosv)sinu, z=wsinv maps the interval Q={(u,v,w) : u, v are [0,2pi] and w is [0,b]} onto this torus. Apply the change of...
8. ### Function of uniform random variable.

Hello this is the problem I'm working on. a voltage X is uniformly distributed in the set {-3,-2,-1,0,1,2,3,4} A. Find the pdf and CDF of the random variable X. for this question I found the pdf as [[pdf=1/7 for -3<=X<=4 and 0 else]] also I found the CDF as [[ CDF= (X+3)/7 for...
9. ### Help with solving for a variable

I have what seems to be a rather simple problem, but my brain is just not quite working right on it. For the equation,Fb = Fs((v – va)/(v + va)) I need to solve for va but I can't quite work through the steps for isolating it to one side of the equation since it rests on both top and bottom of...
10. ### Complex Variable Methods

Integral from -infinity to infinity of (xsin(2x)/(x^2+a^2) the parameters are a>0. I am unclear on how to begin this question... I know that sin(x)=(2u)/(1+u^2) so then dtheta=(udu)/(1+u^2) sin(2x) then equals (4u)/(1+2u^2) but then i got (xu)/((1+u^2)(x^2+a^2)). Now where do I go?
11. ### Discrete vs continuous variable

What type of variable is the number of patients who visit the doctor in one day? My answer is discrete. Please let me know if I'm missing something here.
12. ### Matching moments of distributions of a random variable x and a transformation x1=x^2

My statistics have become a bit rusty. I am puzzled with a problem. Let assume that x is a random variable and can either x ~ Normal(0,1) or x ~ Uniform(a,b) From Normal : E(x) = 0, V(x) = 1 From Uniform : E(x) = 1 / (a+b), V(x) = 12 / ( (b-a)^(2) ) If we want to match the mean and the...
13. ### Isolate a variable

Hi all, I am turning this equation all around and I can't manage to isolate and express g as a function of the other parameters. (A is a known value) A = \frac{1-(\frac{1+g}{1+r})^{n+1}}{1-\frac{1+g}{1+r}} Any hint ? Thank you very much in advance !
14. ### Finding the distribution of the random variable from function?

Hi, Can anyone please find the CDF and PDF of the random variables from the following functions in any way?
15. ### Isolating Variable in Sinusoidal Function

Basically I'm trying to solve for d in f(x)=a*sin[k(x-d)]+c. I have the values of all the other variables so a simpler way of solving it is fine too.
16. ### Variable m is a Slope

Why is m in the equation y = mx + b called a slope? Why is m accepted by worldwide mathematicians as the symbol for slope or gradient?
17. ### Distribution function of random variable

Hi! I would really like to get some help with the following problem: "A man lives by a bus stop from which he takes a bus to his job. The journey takes 20 minutes and the buses comes with a 10 minute interval. One certain morning he plans to be at work at 8:30 and not later. He needs 20 minutes...
18. ### limit of multi variable functions

So we were learning about 2 dimensional domain functions today, and my prof put up a limit. he did some work and then did something I was a bit stumped on for a while: lim_{y\to\0} \frac{0}{y^2} \Rightarrow 0 . Isn't this indeterminate? Would it be 0 because y^2 is not ACTUALLY 0, but simple a...
19. ### pdf for continuous random variable

Hello again everyone, I'm having some trouble understanding an example for a probability density function of a cont. RV. The part I'm not getting is the integrals. I need an elaboration on what is going on with the calculations so I can see what is happening. I assume that it has something to...
20. ### Binomial Random Variable Probabilities

The problems states X is a binomial random variable, n=25 and p=0.8. Asks for the standard deviation of X. Any clue how this would be solved?