Random variable Definition and 268 Threads

Homework Statement A trial consists of throwing two dice. The result is counted as successful if the sum of the outcomes is 12. What is the probability that the number of successes in 36 such trials is greater than one? What is this probability if we approximate its value using the Poisson...

In the page that I attached, it says "...while at the continuity points x of F_x (i.e., x \not= 0), lim F_{X_n}(x) = F_X(x)." But we know that the graph of F_X(x) is a straight line y=0, with only x=0 at y=1, right? But then all the points to the right of zero should not be equal to the limit of...

1. In scanning electron microscopy photography, a specimen is placed in a vacuum chamber and scanned by an electron beam. Secondary electrons emitted from the specimen are collected by a detector and an image is displayed on a cathode-ray tube. This image is photographed. In the past a 4- ...

Hello everyone! I'm looking at the following random variables: $Z_1$ is normally distributed with zero mean and variance $\sigma _1 ^2$ $Z_2$ is normally distributed with zero mean and variance $\sigma _2 ^2$ $B$ is Bernoulli with probability of success $p$. $X$ is a random variable that...

My professor made a rather concise statement in class, which sums to this: E(Y|X=xi) = constant. E(Y|X )= variable. Could anyone help me understand how the expectation is calculated for the second case? I understand that for different values of xi, we'll have different values for the...

Homework Statement 1000 independent rolls of a fair die will be made. Compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively. If the number 6 appears exactly 200 times, find the probability that the number 5 will appear less than 150...

My problem is as follows (sorry, but the tags were giving me issues. I tried to make it as readable as possible): Let X have the pdf f(x)= θ * e-θx, 0 < x < ∞ Find pdf of Y = ex I've gone about this the way I normally do for these problems. I have G(y) = P(X < ln y) = ∫ θ * e-θx...

Work done so far... [FONT=Helvetica]Integrating from 0 to infinity and equating it to 1, we get [FONT=Helvetica](c/2*10^-3) = 1 [FONT=Helvetica]c= 2/1000 [FONT=Helvetica]=0.002 Is it correct? http://www.chegg.com/homework-help/questions-and-answers/-q3136942#[FONT=Helvetica][FONT=Helvetica]

lets say that X is some random variable that takes +1 if rational otherwise -1. at http://tutorial.math.lamar.edu/Classes/CalcI/TheLimit.aspx in example 4, can we consider g(x) as a random variable because it's behaviour is same, right? is random variable really random or just function? I found...

I have the continuous random variable Y, defined such that: Y=3X+2 and the PDF of x is zero everywhere but: f(x)=\frac{1}{4}e^{\frac{-x}{4}}, x>0 I correctly got the mean like so: \mu=E(h(x))=\int^{\infty}_{0} h(x)f(x) and evaluated it to be 10. I am unsure as to how I go about...

I have always struggled in understanding probability theory, but since coming across the measure theoretic approach it seems so much simpler to grasp. I want to verify I have a couple basic things.So say we have a set χ. Together with a σ-algebra κ on χ, we can call (χ,κ) a measurable space...

A problem in this book asks for the most probable value of a random variable x. As far as I know, if a random variable has "most probable value" then it isn't a random variable. The problem is attached. It is the second question in part b. Could the answer be that there is no most probable...

i have this question i do find the distribution like this figure : and i plot the y like this: now i want to find the distribution of y i tried to take the distribution for each interval in Fx(x) like this : but the solution in the book said : who is wrong me or the book...

Homework Statement A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Success with any opponent is independent of previous encounters. The player continues to contest opponents until defeated. What is the probability...

Hi all, I am really confused about the random variables Toss a coin three times, so the set of possible outcomes is Ω={HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} Define the random variables X = Total number of heads, Y = Total number of tails In symbol, X(HHH)=3...

Hi there, I am currently reading Rohatgi's book "An introduction to probabilty and statistics" (http://books.google.de/books?id=IMbVyKoZRh8C&lpg=PP1&hl=de&pg=PA62#v=onepage&q&f=true). My questions concerns the "technique" of finding the PDF of a transformed random varibale Y by a function...

Hey guys, I have a quick question. Suppose X is a chi squared random variable with n degrees of freedom and Y is another independent chi squared random variable with n degrees of freedom. Is X/Y ~ 1 ? Intuitively, it makes sense to me but I'm not too sure.

Homework Statement I must calculate the characteristic function as well as the first moments and cumulants of the continuous random variable f_X (x)=\frac{1}{\pi } \frac{c}{x^2+c^2} which is basically a kind of Lorentzian.Homework Equations The characteristic function is simply a Fourier...

Homework Statement Let f(x)=x/8 be the density of X on [0,4], zero elsewhere. a) Show that f(x) is a valid density and compute E(X) b) Define Y=1/X. Calculate E(Y) c) Determine the density function for Y The Attempt at a Solution a) is just really basic. I've solved that one. b)...

Hi everybody, I try to figure out connections and differences between random variables (RV), random processes (RP), and sample spaces and have confusions on some ideas you may want to help me. All sources I searched says that RP assigns each element of a sample space to a time function. I want...

Homework Statement Suppose X is a discrete random variable whose probability generating function is G(z) = z^2 * exp(4z-4) Homework Equations No idea The Attempt at a Solution I'm thinking that due to the exponent on the z term, that the exp(4z-4) would be the P[X=3] =...

EDIT: Oh and I forgot that $p_Y(y) = 0$ otherwise.

You are given a random exponential variable X: f(x) = λ exp(-λ x). Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X: Y = IP(X), Z = FP(X). Which is the following conditional probability: P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?

Hi, I have a random variable X with some zero-mean distribution. I have a function Y of this r.v. given by something complicated Y=(a+X)^\frac{2}{3} Is there an explicit way of finding the distribution of Y or even its mean? Thanks

About the definition of "discrete random variable" Hogg and Craig stated that a discrete random variable takes on at most a finite number of values in every finite interval (“Introduction to Mathematical Statistics”, McMillan 3rd Ed, 1970, page 22). This is in contrast with the assumption that...

Homework Statement In the winter, the monthly demand in tonnes, for solid fuel from a coal merchant may be modeled by the continuous random variable X with probability density function given by: f(x)=\frac{x}{30} 0≤x<6 f(x)=\frac{(12-x)^{2}}{180} 6≤x≤12 f(x)=0 otherwise (a)...

Suppose that X is a random variable distributed in the interval [a;b] with pdf f(x) and cdf F(x). Clearly, F(b)=1. I only observe X for values that are bigger than y. I know that E(X|X>y)=\frac{\int_y^b xf(x)dx}{1-F(y)}. Moreover, \frac{∂E(X|X>y)}{∂y}=\frac{f(y)}{1-F(y)}[E(X|X>y)-y] I...

Edit: I have to think more about this, I'll post later.

1. Homework Statement During a typical Pennsylvania winter, I80 averages 1.6 potholes per 10 miles. A certain county is responsible for repairing potholes in a 30 mile stretch of the interstate. Let X denote the number of potholes the county will have to repair at the end of next winter. 1...

I know the E[X] = Integral between [-inf,inf] of X*f(x) dx Where X is normally distributed and f(x) is the PDF How do I find the expectation of X4? Bare with me because I'm useless in Latex So far what I've done is written the integral as Integral between [-inf,inf] of X4*f(x) dx...

Homework Statement Find the Mean and Variance of Random Variable Z = (5x+3) Using data set:Using: & The Attempt at a Solution

Dears, If a random variable is generated with the pdf of p(f) = 1/(f^x), how can I derive the upper bound or lower bound of the random variable? Thanks,

Dears, If a random variable is generated with the pdf of p(f) = 1/(f^x), how can I derive the upper bound or lower bound of the random variable? Thanks,

I am wondering if I can find a decomposition of Y that is absolutely continuous nto two i.i.d. random variables X' and X'' such that Y=X'-X'', where X' is also Lebesgue measure with an almost everywhere positive density w.r.t to the Lebesge mesure. My main intent is to come up with two i.i.d...

There are plenty example of functions are random variables from my class note. I only interested of thinking up functions are not random variables. If you know functions are not random variables please please reply this post. This class is about set theory, probability measure, Borel...

Homework Statement Show that if X is a bounded random variable, then E(X) exists.Homework Equations The Attempt at a Solution I am having trouble of finding out where to begin this proof.This is what I got so far: Suppose X is bounded. Then there exists two numbers a and b such that P(X > b)...

Homework Statement A Normally distributed random variable with mean μ has a probability density function given by _ρ_...*...((-ρ2(x-μ)2)/2δ) √2∏δ|...e^ Homework Equations Its standard deviation is given by: A)ρ2/δ B)δ/ρ C)√δ|/ρ D)ρ/√δ| E)√δ|/2ρ The Attempt at a Solution...

Going over my Lecture Notes my Lecturer as Started with Show that a Gaussian Distribution Corresponds to a CTS random variable. Then she has i) Taken the f(x) = [p.d.f] and shown a) f(x) >= 0 for all x member of real numbers. b) Integral over all real numbers = 1 ii) Found the M.G.F then...

Homework Statement A random variable X has probability generating function gX(s) = (5-4s2)-1 Calculate P(X=3) and P(X=4) Homework Equations The Attempt at a Solution Ehh don't really know where to go with one... I know: gX(s) = E(sx) = Ʃ p(X=k)(sk) Nit sure how to proceed.. Any help would...

Homework Statement a) Let X1, X2, ...XN be a collection of independent Bernoulli random variables. What is the distribution of Y = \sumNi = 1 Xi b) Show E(Y) = np Homework Equations Bernoulli equations f(x) = px(1-p)1-x The Attempt at a Solution a)X1 + X2 + ... + XN = p...

Determine constant c so that random variable will have a t distribution? Homework Statement Suppose that five random variables x1, x2, x3, x4, x5 are independent and have normal distribution N(0,1). Determine a constant c such that the random variable c*(x1+x2)/\sqrt{x_3^2 + x_4^2 +...

Homework Statement Given a random variable X with a known distribution (e.g. a beta distribution), find the distribution of f(X) = X^2 + X The Attempt at a Solution I've tried the normal approaches: the standard transformation theorem; conditioning on X; Laplace transformation, etc...

Hello, I have a really tough time understanding this concept although this isn't anything more complex than a composition of functions. I have a done example from my book that I am trying to interpret. p_\xi (x)=\frac{1}{\pi} for an interval between [0,∏] The...

Homework Statement If Z has a standard gaussian distribution then what is the distribution of Z2 and what is its mean? The Attempt at a Solution Let T = Z2 Then we can get that pdf T = e-T/2(1+1/T) x (1/√(2∏T) I am not sure if this is correct and don't know how to find the...

Hi all I'm looking for solving this problem to find the closed form solution if it is possible: Y=\frac{1}{X} Where X is uniform random variable > 0 I know the expected value for X which is \overline{X} is there a method to find the expected value of Y which is \overline{Y} in term of...

Hey, I have a pdf of a random variable Z given. I am being asked to calculate what the moment generating function of a r.v Y= Z + c will be where c is a constant in ℝ I tried to calculate it in the following way: \int^∞_0 e^{(z+c)t} f(z+c)dz where f(z) is an exponential pdf with...

For X ~ N(μ, σ), what is P[|X-μ] < σ] in terms of the Q function? I know that P[|X-μ] < σ] can be decomposed into P[X > -σ + μ] + P[X < σ + μ] I'm not sure what to do next. i know P[X < σ + μ] can be expressed as 1 - phi(σ + μ - μ / σ) = Q(1), but I'm not sure how to approach P[X > -σ + μ]. I...

Let X and Y be independent and uniform on {1, 2, ... M} Find P(X > Y) so i know that P(X = x) = 1/M and P(Y = y) = 1/M i don't understand how Find P(X > Y) = (M+1)/2M

Homework Statement The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 70000 miles and a standard deviation of 5000 miles. A: What is the probability that...

Hi. I choose randomly a one word, and I decided to choose a word blue. Let random variable x be a length of the word blue. What is expected value and variance of a word blue? So, random variable x = 4. E(X) = [SIZE="5"]Ʃ xi fX(xi) i:xi∈S x1 + x2 + x3 + x4 = 10...