1. J

    Continuous Function

    (cos x)/(x - (pi/2)) I don't Understand why this function is continuous because when I plug pi/2 in x, it causes problems.
  2. J

    Piecewise-defined Function

    Determine where f is continuous. f(x) = (sin x)/x if x not = 0 f(x) = 1 if x = 0 Is it correct to say f is continuous everywhere?
  3. L

    Continuous odd function

    Can someone please help me with this one :) Let f :[-1,1] → ℝ be a continuous odd function. Show that for every ϵ >0 exist such real numbers a1,a3,...,a2n+1, so that ∣a1x+a3x3+...+a2n+1x2n+1 − f(x)∣ < ϵ for every x ∈ [-1,1]. Thank you!!(Happy)
  4. A

    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.
  5. M

    Conditional p.d.f. of a continuous bivariate distribution

    Consider the random variable X and Y with joint probability density function as: f(x,y) = 24xy for 0<x<1, 0<y<1, 0<x+y<1 Find the conditional p.d.f. of X given Y = 0.5 Here's what I've got: f_{Y}(y)=\int_{-x}^{1-x}24xydx=-24y^2+12y and then...
  6. M

    Topological space and continuous function

    Let $X$ be a toological space. Suppose that $f$ and $g$ are continuous maps $X\to \mathbb{R}$. Define the function $(f+g)(x)$ by $(f+g)(x)=f(x) + g(x)$. Show that $$(f+g)^{-1}((a,b))=\bigcup_{s,t\in \mathbb{R}}f^{-1}((s,t))\cap g^{-1}((a-s,b-t))$$ and deduce that $f+g$ is continuous. Here's...
  7. M

    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...
  8. D

    peicewise continuous function

    I am confused about piecewise continuous function with their different intervals. Does an interval have to be continuous on its own interval only?. So say a left interval does not have to have the the same limit at the point where the right interval begins.
  9. A

    continuous function

    I am working through David Brannans 1st course in mathematical analysis and am currently dealing with continuity , I am just trying to understand definition of continuous function The definition given is : A function is defined on an interval I that contains c as an interior point is...
  10. H

    show that the functions are continuous

    show that the following functions f are continuous: a) f(x,y) = x+y b) f(x,y) = x^2 *y +y c)f(x,y) = ((x*y)/(1+x^2+y^2)) d) f(x,y) = e^-x sin(x+y) e) f(x,y,z) = x^2 + y^2 + z^2 I know all of them are continiuos on whole R except nr.c which is cotinous on R except 1+x^2+y^2 = 0 Because all...
  11. R

    Is the Function Continuous

    Given f(x) = (x + 2)/(x - 2), is the function continuous at x = 2? Is there an asymptote at x = 2? Is this a 0/0 case?
  12. H

    continuous valued output

    what is the meaning of continuous valued output?
  13. R

    Need help evening-out seperate continuous measures into one conclusive variable (RFM)

    Hi all, I'm currently developing a RFM-model for one of our clients. It's manually adapted here and there since we're not dealing with an e-commerce company. However, the model is conceptually the same. My question is the following; I create calculated units for the 3 following variables...
  14. A

    Determine whether the function is uniformly continuous

    I have the question determine whether f(x)=(4x-3)/(x-2) is uniformly continuous on the open interval (1,2). I have only answered these types of questions with closed intervals so I'm not sure how to proceed? Thanks, Alex
  15. A

    Finding values where the function is continuous

    What does the comment in green ink mean? (refer to image)
  16. J

    Continuous function f:R→R such that f(f(x))=−x?

    Continuous function f:\mathbb{R}\to\mathbb{R} such that f(f(x)) = -x? Find a continuous function f: \mathbb{R} \to \mathbb{R} satisfying (f(x)) = -x Continuous function f:\mathbb{R}\to\mathbb{R} such that f(f(x)) = -x? for all x \in \mathbb{R}. I was thinking of letting f be a periodic...
  17. D

    Continuous Time Markov Chain

    Hi, I have a general question. Suppose that you have a two state markov chain S (suppose the states are 0 and 1). The transition probability of it, over an infinitesimal interval dt is: \left[\begin{array}{cc}1-\lambda_{H}dt & \lambda_{H}dt\\\lambda_{L}dt & 1-\lambda_{L}dt\end{array}\right] In...
  18. C

    Continuous RV Probability

    Pick four numbers independently at random from [0, 1] and let Y be the second largest. Find P(Y > 1/2). Since we are picking the numbers randomly and independently, can we just say let's chuck the largest and look at the max of three numbers? Or in other words, let's just consider three numbers...
  19. D

    determine the constant in continuous random variable

    Can someone check thru my working? I cant find mymistake... The ans is b =4
  20. D

    finding value of unknown in continuous probability function

    i am having problem with part a , the question give f(x) which is probablity density function. my friend gives solution as follow: first , he integrate from 10 to 30 then , he equate f(20) using 0.01x - p and q-0.01x i dont think this is correct. since the graph of f (x) may not be...