Exponential Definition and 1000 Threads

Suppose I have several exponentially distributed random variables, each of them representing the probability that some particular event occurs within some amount of time. I can't seem to come up with any intuition as to how to combine those density functions (or distribution functions) to...

I am looking a formula to compute the derivitative of e^{a x^2} with respect to x n times, where a is a constant. \frac{d^n}{dx^n}e^{a x^2} I am going to find the result of above derivitative when x -> 0.

Homework Statement The time between calls to a corporate office is exponentially distributed with a mean of 10 minutes. What is the probability that there are more than three calls in one-half hour? Homework Equations F(x) = P(X <= x) = 1 - e^-(lamba*x) The Attempt at a Solution...

Homework Statement 1. \int^{\infty}_{-\infty}e^{-ax^2 - bx^{\frac{5}{2}}}dx 2. \int^{\infty}_{-\infty}x^ne^{-ax^2 - bx^{\frac{5}{2}}}dx (n is integer) Homework Equations Does anyone can give me the integral in the closed form or introduce any useful references? Thank you.

Homework Statement Find the exponential function that passes through the points (2, 1) and (5, 7). Homework Equations y= Ce^ (kt) The Attempt at a Solution I can only get as far as substituting in 2 for t and 1 for y, then I'm completely stuck.

Homework Statement A curve passes through the point (0,6) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? Homework Equations Y=Yoe^kx is a solution of (dy/dx)=ky, where k is constant The Attempt...

In general what do you do when some kind of data is missing from some data that follows exponential distribution. For example, say 3 observations are made by an instrument where x1=5, x2=3, but for x3 the instrument can not give a specific answer because it can't measure past 10. So the only...

Homework Statement X is exponentially distributed. 3 observations are made by an instrument that reports x1=5, x2=3, but x3 is too large for the instrument to measure and it reports only that x3 > 20 . (The largest value the instrument can measure is 10) a)What is the likelihood function...

I am in a trouble to work out the sum, i.e. "sum of exponential of[-a^2.n^2]" , where, n is an integer... and sum over 1 to infinity, and "a" is "not small...", I've calculate two asymptotic behaviours , i,e when "a<<1" , in this case I've integrated it and have got, sqrt(pi)/2a-1, and in the...

Homework Statement Solve the equation: (x+xy^{2})dx + e^{x^{2}}y dy =0 Homework Equations n/a The Attempt at a Solution i) xdx(1+y^{2}) = -e^{x^{2}}y dy (multiply both sides by 2 to prepare for integration: ii) \frac{-2xdx}{e^{x^{2}}}= \frac{2y dy}{1+y^{2}} integrate and get: iii)...

¡¡get matrix exponential Please! Homework Statement I have a exam and i don't know how get matrix exponential: | 2*t t| | 3*t -t| it is a 2x2 matrix. where 't' is not a constant ,it is a variable somehere could help me,please. Homework Equations The Attempt at a Solution...

Homework Statement This isn't a problem, I'm just obsessed with analyzing a trig/exp equation algebraically instead of with a calculator. 8*sin(t) - 16*cos(t) = 9*exp(-t/2) Homework Equations See part (1.) above... The Attempt at a Solution I tried converting the exp part...

Can a convenient value for a be found without resorting to substituting numerical values for h in this expression? EDIT: I am trying to indicate, "as h approaches zero". EDIT: neither of the formattings worked; hopefully someone understands what I am asking...

Homework Statement I'm new to integration, and was attempting the integral of ex with respect to x. Homework Equations \intex dx The Attempt at a Solution Should I keep it in the format y=ex so that I use this in the calculation of the area? Or should I convert to ln y? I got stuck...

Hi! I want to know how to intergrat e^(-(x^2)/2) . Someone told me to use the intergration of e^x= 1+ x + (x^2) /2!+ ...(X^n)/n! ... is that sounds right?? and if it is i got pi as an answer for e^(-(x^2)/2) , is that the right answer?

Homework Statement Determine the period in which y = Cekt changes by a factor of q. I have no idea what it is asking.. find t when k=q?

Theorem Let A be a square matrix nXn then exp(At) can be written as exp(At)=\alpha_{n-1}A^{n-1}t^{n-1} + \alpha_{n-2}A^{n-2}t^{n-2} + ... + \alpha_1At + \alpha_0 I where \alpha_0 , \alpha_1 , ... , \alpha_{n-1} are functions of t. Let define r(\lambda)=\alpha_{n-1}\lambda^{n-1} +...

Hi, I'm trying to solve the following: f(x) = \int^\infty_{-\infty}ce^{yx-y^2/2} dy where c is a constant My only idea thus far was that since it is an even function, the expression can be simplified to: = 2c\int^\infty_0 e^{y(x-{1/2}y)} dy but I'm stuck here. Anyone know how to do...

Homework Statement Show that (ez)*=ez* note: * is the conjugate Homework Equations The Attempt at a Solution So I wasn't sure what form to put this in...either in exponential reiѲ or cos Ѳ + isin Ѳ...Either way, I think I'm just making it too easy... Please help!

Homework Statement What is the derivative of ex3? also what is the derivative of (ln1/x)2Homework Equations The Attempt at a Solution is it 3x2e3x2? 2(ln1/x)(x)?

Hello, In a paper, the authors defined an exponential Random Variable (RV) as X_1 \mbox{~EXP}(\lambda) where \lambda is the hazard rate. What will be the distribution of this RV: f_{X_1}(x)=\lambda e^{-\lambda x} or f_{X_1}(x)=\frac{1}{\lambda} e^{-\frac{x}{\lambda}} Thanks in advance.

Homework Statement The problem asks to graph tangent lines to the given function y = (ln(x)/x, and gives the points (1,0) and (e, 1/e) Homework Equations The Attempt at a Solution I got the answer by taking the derivative and finding the slope, and at the point (e,1/e) the...

Homework Statement Hello. I'm afraid it's quite a simple and unexciting problem I have. Basically, I can't remember how to rearrange the equation for an exponential curve: The capacitor has a capacitance of 0.63 mF and the resistance in the discharge circuit is 2.4 kΩ. (i) Calculate...

1. It is estimated that x years from now the value of an acre of farmland will be increasing at the rate of \frac{0.4x^3}{sqrt(0.2x^4+8000)} dollars per year. If the land is worth 500 per acre, how much will it be worth in 10 years? 2. Use integral Since the the function of money...

Homework Statement The distance between major cracks in the highway follows an exponential distribution with a mean of 5 miles. What is the probability that there are two major cracks in a 10 mile stretch of the highway? Homework Equations exponential dist: f(x) = Le(-Lx) where L...

I have seen the following identity used. Exp[iw/2]-Exp[iw/2]=Exp[iw]-1 I can't find this in any book and I can't prove it myself. The left side equals 2isin(w/2) The right side equals cos(w)+isin(w)-1 On the face of it, that seems to make the identity absurd How can one go about proving...

Homework Statement Consider a horizontal slab of air whose thickness(height) is dz. If this slab is at rest, the pressure holding it up from below must balance both the pressure from above and the weight of the slab. Use this fact to find an expression for Dp/dz, the variation of pressure...

Hello Physics Forums, I sometimes come across statements like this (from http://beige.ucs.indiana.edu/B673/node62.html" ): Now assume a solution of the following form: x(t) = Aeat What is the motivation/background to make such an assumption? In this case the equation to be solved is x''...

Homework Statement Derive (from the equation of motion of a neutral gas and an assumption of constant gravitational field) an expression showing why the concentrations of neutral molecules decrease approximately exponentially with increasing altitude, and why the concentration of atomic oxygen...

Solve for real-valued x, e-aX + e-bX = 1, where a and b are arbitrary known constants > 0. For example, e-48.12/50 + e-48.12/100 ~ 1.00 In this case X = 48.12 (to two decimals), a = 1/50 and b = 1/100. For any specific values of a and b, a computational solution can easily be determined...

Homework Statement Viruses are reproducing exponentially, while the body eliminates the viruses. The elimination rate is constant, 50000 per hour. I decided to take down on the minute level, so it would be 50000/60. Pinitial is 10^6 k is ln(1,6)/240, since the growth rate is 160% in 4...

Homework Statement Viruses are reproducing with rate of k ,in t minutes, the function is: f(x) = Po x e^(kt) However there is an elimination rate of a viruses per minute. Homework Equations The Attempt at a Solution We can't say that the new function will be: f(x) = Po x e^(kt)...

It is known that \[\sum\limits_{k = 0}^\infty {\frac{{N^k }} {{k!}}} = e^N \] My question is \[\sum\limits_{k = 0}^M {\frac{{N^k }} {{k!}}} = ? \] where $M\leq N$ an integer. This is not an homework

Homework Statement e^(2x+9) - 4e^x -5 = 0 Homework Equations The Attempt at a Solution I changed this into: e^(2x+9) =4e^x + 5 I took logarithm of both sides: 2x+9=ln(4e^x +5) but i don't know what to do with the right hand side. what will be the easiest way to solve this...

Homework Statement A=\begin{bmatrix}-1 & 2 & 0\\-2 & -1 & 0\\ 0 & 0 & -3\end{bmatrix} Use matrix A and compute exp(tA) explicitly. Homework Equations I am having trouble figuring out how to start this. I know how to look at each component of matrix A and to use exp(tA)=I+tA...

Homework Statement Integrate the following equation for average energy from -infinity to infinity \int(c*x^4)*(e^(-c*x^4)/KT)dx Homework Equations c, K, T are constants \int(e^(-c*x^4/KT)) = (KT/c)^(1/4)*(2\Gamma(5/4)) The Attempt at a Solution I tried using integration by parts...

Homework Statement let be A_{i,j} a Hermitian Matrix with only real values then \int_{V} dV e^{iA_{j,k}x^{j}x^{k}}= \delta (DetA) (2\pi)^{n} (1) Homework Equations \int_{V} dV e^{iA_{j,k}x^{j}x^{k}} = \delta (DetA) (2\pi)^{n} The Attempt at a Solution the idea is that...

Need help solving this. \int^{\infty}_{-\infty} e^{\frac{-x^{2}}{\sigma^{2}}} e^{-ikx}dx That's the integral of the product of the exponentials , couldn't get latex to make it look right. Supposedly usefull information(I can't see how); \int^{\infty}_{-\infty}...

Its true that if you integrate an exponential function from some time t0 to infinity it will converge to a finite value. However, is the same true if it is multiplied by say t, t^2, t^3,t^n. i.e. t*exp(-t) for example. the exp is decaying to zero faaster than t is, so it goes to zero...

Homework Statement Suppose two exponential functions, f(x) and g(x) are symmetric with respect to x = 2. f(x)=a^{bx-1} g(x)=a^{1-bx} Prove f(2) = g(2) Homework Equations The Attempt at a Solution This isn't actually a problem. This is a property used to solve a different...

Is the series \sum_{n=0}^{\infty}\frac{z^n}{n!} uniformly convergent for all z in the complex plane? It is uniformly convergent for all z in any bounded set, but the complex plane is unbounded. My instinct is that it is NOT uniformly convergent for all z in C. This is not homework.

Hi folks, hope somebody can help me understand this one please? Gven an expression i = ia-ic = icorr(exp(n/Ba)-exp(-n/Bc)), we are told that if -n<<Bc then exp(-n/Bc) tends to 0 & the equation becomes i (is approx) = ia = icorr exp(n/Ba). I find that exp(-n/Bc) tends towards 0 if I...

let be the exponential sum S= \sum_{n=1}^{N}e( \frac{f(x)}{p}) e(x)= exp( 2i \pi x) my conjecture is that since the complex exponential takes its maximum value '1' when x is equal to an integer then Re(S)= \Pi (f,N) with \Pi (f,N) is the number of solutions on the interval...

Homework Statement I am in the process of doing a physics problem with a differential equation that has the form: y = Acos(kx) + Bsin(kx) According to my notes, this can also be written as y =Aejkx + Be-jkx, unfortunately I just don't see how to write the original equation like that...

Homework Statement Series k=1 to k=Infinity of: k^2/k! a) e b) 2e c) (1+e)(e-1) d) e^2 e) Infinity Homework Equations e^x = Series from n=1 to n=Infinity of: x^n / n! The Attempt at a Solution I was guessing this would end up being C but the answer is infact B. As...

Exponential Attenuation and Beta Particle Range (solved) Homework Statement I am given a beta emitter and its atomic mass, as well as the atomic mass of its daughter, which have a difference of 0.0034 amu. I am to determine the range of the particles in air. Homework Equations I am given...

Homework Statement 1) 5x+4-5x-1<24 2) 2x+2-1>=22x+3 3) 21-x-2x+1/2x-1<0 Homework Equations At the 2nd I do like this: 2x+2-22x>=4 divide by 2 2x+1-22x-1>=2 x+1-2x+1>=1 -x>=-1 divide by (-1) x=<1 but when i put 0 in x the inequation is incorrect, what I have mistake, please...

Homework Statement Please , can anybody help me to do these and to explan to me? I tried tried, but i can't do anything. 1. 4x-1 + 4x + 4x-1=84 2. 15 * 2x+1 + 15 * 2 x-1 =135 3. 8x + 18= 2* 27x 4. 3x-8*3x/2 +15=0 5. 5x - 53-x=20 Homework Equations At the 5th i do...

Homework Statement Howdy, Given a matrix \left[\begin{array}{ccc}x_{11} & x_{12}\\x_{21} & x_{12}\end{array}\right] Which has the exponential matrix e^{t\cdot a} When given the eqn x'= Ax + b where b = \left[\begin{array}{c}b_1 \\ b_2\end{array}\right] I know that had it only...

Suppose I have a sample X_1, ..., X_n of independently, identically distributed exponential random variables. One result I deducted was that the ratio of any two of them (eg. X_1 / X_2) is independent of the sample average 1/n * \sum_{i=1}^{n} X_i. (Aside: that ratio, as a random variable...