A robotic arm in an amazon shipping center places packages into shipping containers. Each container is packed with 100 packages. Let X; denote the weight of the ith package in a given container. Suppose that the X; are generated iid from a distribution with E[X] = 1 and Var[X] = .05². Let W be the total weight of the container (assume the %3| container itself has 0 weight). Find an asymptotic approximation to P(W > 100.4).

Q: Determine for what values of k the integral ∞∫1dxxk(k>0,k≠1) converges.

A:

Q: Let X1, X2,...,X, be a set of independent random variables each following the distribution with pdf…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q8 Marginalize the joint probability PMF's. mass function of X and Y in the previous qusetion to get…

A: Introduction: Consider a jointly distributed pair of random variables, X and Y, with joint…

Q: Let X be a continuous random variable with PDF x> 0 fx(x) ={0 0. otherwise Find E[X], Var[X] and…

A: Simple integration

Q: Determine the convergence state of the integral using the comparison test w? dw w3 – 1

A: Comparison test states that : If fx≥gx≥0 on the interval [0,∞) then, If ∫a∞fxdx converges then so…

Q: Find the upper darboux sum of f(x)=ln(x) for n equal subintervals on the partition [1,2].

A: The given function is f(x)=ln(x). here, x∈1,2 and P=nn,n+1n,...,n+nn be the partition of [1, 2] in n…

Q: Suppose I flip a coin n= 100 times and I obtain heads X=44 times. Assuming the coin is fair,…

A:

Q: find the convergen e inteY Val and vadins d Vadius: test the end point of interval: vn (メー2) 37

A:

Q: Let X be a continuous random variable with a pdf f(x) = { kx5     0≤x≤1,             0…

A:

Q: where Oso, using the factori Zation theorem, Tn = #x;, is a sufficient stati Show That for 0.

A:

Q: If  f(x) = 5x2 − 4x, 0 ≤ x ≤ 3,  evaluate the Riemann sum with n = 6, taking the sample points to…

A: Definition used -            Riemann sum using right endpoints-…

Q: Expand in ascending powers of x up to and including the term in x. 7x assuming x = 25 estimate v13…

A: Given: 1+x1-7x12

Q: Show that for every positive function f on R there is a monotone increasing sequence of integrable…

A: We need to show that for every positive function f on ℝ there is a monotoneincreasing sequence of…

Q: Suppose that a sequence of mutually independent and identically distributed discrete random…

A: Given  X~Pois(θ)

Q: The following improper ategral(r- De **!dx converges to3e convergesO optich

A:

Q: Calculate the probability of finding the particle within the finite wall of the box when the…

A:

Q: Let X be a continuous random variable with pdf f(x). If f(x) = 0 for x 0, P(X >a) < a where μ-…

A: Continuous Random Variable: A continuous random variable is a variable whose value can be obtained…

Q: Iff (t) is the unconditional density of the time of failure of a system and h(t) is the hazard rate…

A:

Q: Suppose that X₁, X₂, X3 X is a random sample of n from population X which has a chi- square…

A: Given that  X1,X2,.....,Xn is random sample of "n" from the population X  Xi follows Chi-square…

Q: Use a Riemann sum with m = n = 2 to estimate the value of 5xe-XY dA, where R = [0, 2] x (0, 1). Take…

A:

Q: A poll showed that when a sample of people in a certain country were asked whether they were…

A: According to our guidelines we are only allowed to answer three sub-parts   (h) Since we know that :…

Q: Suppose that X₁, X₂, X3.....X is a random sample of n from population X which has a square…

A: Given Xi~chi square distribution with one degree of freedom, and they are random sample…

Q: Show that the characteristic function of a ran- dom variable having the binomial density is, ,(0) =…

A: A random variable x~Binomial(n,p)P(x)=(nx)×px×(1-p)n-x ; x=0,1,...,nwhere p is a parameter

Q: Suppose that X and Y are independent and both follow an exponen- tial distribution with rate…

A:

Q: Compute the point-wise limit of (fn) and determine if they converge uniformly on given intervals. 1.…

A:

Q: 1 Evaluate the integral of ₁dx for P > 1, and determine whether it is convergent or divergent. xP

A:

Q: for a <r <b (and zero elsewhere) such that f is a PDF of a continuous random variable with expecte…

A:

Q: Suppose that the following probability density function (pdf) for the random variable X: f(x:0) =…

A: f(x)=θ(1+x)-(1+θ)               =exp[lnθ-(1+θ)ln(1+x)]       =exp[lnθ-ln(1+x)-θln(1+x)] So the…

Q: Find the average power of the random process X(t) which has the power spectral density |@< 4n Sxx…

A:

Q: A random process is defined as X (t) = A. sin (@ t + 0) where A is a constant and O' is a random…

A:

Q: The pdf of x is defined as: K f(x)= - A<xS A |2E – Kx² Where, E is the parameter and K is the…

A: Cumulative Distribution Function  is the probability of occurrence of various events together within…

Q: Suppose you have the following random sample with n independent obser- vations: iid X1, X2,..., Xn…

A:

Q: The Exponential pdf for continuous random variable Y takes the form -y/B y > 0 fV) = for B > 0. y…

A: Solution

Q: Suppose (y/) ~ Poisson(0). Find Jeffrey's prior density for 0.

A:

Q: Assume the service time of a customer at a supermarket follows a Pareto distribution with minimum…

A:

Q: If X has a standard normal distribution (X ∼ N(0, 1)), then the characteristic function of X is…

A: From the given information, X has a standard normal distribution. That is, X ∼ N(0, 1) with the…

Q: The spectral density of a WSS random process X(1) is given by Sxx (@) XX o* +13@ + 36 Find the…

A:

Q: Find the critical value of t for a t-distribution with 30 degrees of freedom such that the area…

A:

Q: Suppose that X is the length of time (in minutes) that a customer queues in a bank. The probability…

A:

Q: If f(x) = e^ – 7, 0 < x < 2, find the Riemann sum with n = 4 correct to six decimal places, taking…

A:

Q: Use the integral test to determine if E el/k is convergent. Show that the hypotheses of the integral…

A: Given that, ∑k=1∞e1kk2 We have an integral test that if ∫1∞f(x) dx converges, then ∑ ann=1∞…

Q: Determine the values of p for which f(x)da converges where f(x) = = 1-e-z TP

A: Here, in the question for what value of p the integral is convergent. The simple improper integral…

Q: If f(x) = ex – 1,0 < x < 2, find the Riemann sum with n = 4 correct to six decimal places, taking…

A:

Q: The continuous random variable, X, has the probablity density function given below. nx for 0 < x <…

A:

Q: If f(x) 2x - 7,0 < x< 3, evaluate the Riemann sum with n = 6, taking the sample points to be…

A: Given function fx=2x2-7, 0≤x≤3 The objective is to evaluate the integral ∫032x2-7dx with n=6 using…

Q: If f(x) = 3x2 - 8x, 0 sxs 3, evaluate the Riemann sum with n = 6, taking the sample points to be…

A: solution

Q: Suppose that X has a continuous distribution with the following probability density function Then…

A:

Q: Suppose that X is a continuous unknown all of whose values are between -5 and 5 and whose PDF,…

A: It is given that the X is a continuous random variable with pdf f(x) = c( 25 -x2 ) , − 5 ≤ x ≤ 5 ,…

Q: If f(x) = In(x) – 1, 1<x < 4, evaluate the Riemann sum with n = 6, taking the sample points to be…

A: Given that      f(x) = ln(x) - 1, 1&lt;= x &lt;= 4  Here we have to evaluate the Riemann sum with…

Q: Perform a testto determine if. S a J y converges diverges or

A: