Prove the ratio test . What does this tell you if exists?
(Ratio test) If
for all sufficiently large n and some
r < 1, then
converges absolutely; while if
for
all sufficiently large n, then
diverges.
Prove the ratio test . What does this tell you if exists? (Ratio test) If for all...
A Pareto distribution is often used in economics to explain a distribution of wealth. Let a random variable X have a Pareto distribution with parameter θ so that its probability distribution function is for and 0 otherwise. The parameters and are known and fixed; is a constant to be determined. a) Assuming that find the expected value and variance of ? b) Show that for 3 ≥ θ > 2 the Pareto distribution has a finite mean but infinite variance,...
Suppose that is a bounded function with following Lower and Upper Integrals: and a) Prove that for every , there exists a partition of such that the difference between the upper and lower sums satisfies . b) Furthermore, does there have to be a subdivision such that . Either prove it or find a counterexample and show to the contrary. We were unable to transcribe this imageWe were unable to transcribe this image2014 We were unable to transcribe this...
Please prove this, thanks! 2. Let {xn n21 be a sequence in R such that all n > 0. If ( lim supra) . (lim supー) = 1 Tn (here we already assume both factors are finite), prove that converges.
One characteristic measured about high schools is the percent free lunch, which is the percentage of the student body that is eligible for free and reduced-price lunches. The top 100 schools, grouped according to their percent free lunch, is as follows. Percent free lunch (x) Number of top 100 ranked high schools 46 20 12 10 12 If stratified random sampling with proportional allocation is used to select a sample of 25 high schools, how many would be selected...
sin 0, cos 0 Name the quadrant in which the angle lies We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Show that a bounded and monotone sequence converges. Here a sequence is called monotone, if it is either monotone increasing, that is for all or monotone decreasing, in which case for all . in Sn=1 An+1 > an neN an+1 < an We were unable to transcribe this image
Let X be a banach space such that X= C([a,b]) where - ab+ with the sup norm. Let x and f X. Show that the non linear integral equation u(x) = (sin u(y) dy + f(x) ) has a solution u X. (the integral is from a to b). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
Let f(x)= if , if if a) What is the fomain of f(x)? Write in interval notation. b) Determine the y-intercept of the function, if any. Make sure to justify your answer. c) Determine the x-intercepts of the function, if any. Justify your answer. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
Prove, or give a counter example to disprove the following statements. a) b) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Negative binomial probability function: is the mean is the dispersion parameter Let there be two groups with numbers and means of 1) Write down the log-likelihood for the full model 2) Calculate the likelihood equations and find the general form of the MLE for and 3) Write down the likelihood function in the reduced model (ie. assuming ) and derive the MLE for in general terms 4) Using the above answers only, give the MLE and standard error for where...