Let X 1 , X 2 , X 3 , be a sequence of random variable
Question:
Let X1, X2, X3, ⋯ be a sequence of random variable such that
where λ > 0 is a constant. Show that Xn converges in distribution to Poisson(λ).
Transcribed Image Text:
(MA). n Xn Binomialn, for n E N, n>d,
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (2 reviews)
By Theorem 71 it suffices to show that lim Px k Pxk n We hav...View the full answer
Answered By
Madhvendra Pandey
Hi! I am Madhvendra, and I am your new friend ready to help you in the field of business, accounting, and finance. I am a College graduate in B.Com, and currently pursuing a Chartered Accountancy course (i.e equivalent to CPA in the USA). I have around 3 years of experience in the field of Financial Accounts, finance and, business studies, thereby looking forward to sharing those experiences in such a way that finds suitable solutions to your query.
Thus, please feel free to contact me regarding the same.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Introduction To Probability Statistics And Random Processes
ISBN: 9780990637202
1st Edition
Authors: Hossein Pishro-Nik
Question Posted:
Students also viewed these Business questions
-
Let Xn be a sequence of random variables that converges in distribution to a random variable X. Let Yn be a sequence of random variables with the property that for any finite number c, Show that for...
-
Let X 1 , X 2 , X 3 , be a sequence of random variable such that where > 0 is a constant. Define a new sequence Y n as Show that Y n converges in mean square to , i.e., Y n m.s. . Xn Poisson (n),...
-
Let X 2 , X 3 , X 4 , be a sequence of random variable such that Show that X n converges in distribution to Exponential(1). Fxn (x) = nx (1-(1-4) 0 x > 0 otherwise
-
Consider the following differential equation describing a plug flow bioreactor: dy --Dy+py dt dz -(4-2)D-2uy dt where D = 0.4, 0.52/(0.1+),and the initial conditions are y(0) = 1 and z(0) = 4. a)...
-
Given that a portfolios return has a mean of 12% and a standard deviation of 14%, find the end points of its 95% confidence interval, assuming a normal distribution." "The answers may be: a) -2% and...
-
The accompanying diagram shows the interest rate on one-year loans and inflation during 19982013 in the economy of Albernia. When would one-year loans have been especially attractive and why?...
-
The central difference approximation of \(d x / d t\) at \(t_{i}\) is given by a. \(\frac{1}{2 h}\left(x_{i+1}-x_{i} ight)\) b. \(\frac{1}{2 h}\left(x_{i}-x_{i-1} ight)\) c. \(\frac{1}{2...
-
Two or more items are omitted in each of the following tabulations of income statement data. Fill in the amounts that aremissing. 2006 2007 2008 $290,000 $ $410,000 Sales Sales returns Net sales...
-
The adjusted trial balance of Gibson Company for the year ended December 31, 2024, is as follows: Cash Accounts Receivable Notes Receivable Merchandise Inventory Equipment Allowance for Doubtful...
-
Let X 2 , X 3 , X 4 , be a sequence of random variables such that Show that X n converges in distribution to X = 1. Fx, (x) = en(x-1) 1+en (2-1) 0 x>0 otherwise
-
An engineer is measuring a quantity q. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and reports the average of the measurements as the...
-
An instructor wishes to see if the answers to his true/false final exam are random. The answers are shown. Test the claim at = 0.05. F F T T T F F F T F T T F F F F T T F F T T F F F T F T T T
-
Would you support the idea of a government issued Digital currency? Why ? and why not?
-
Discuss the dynamic organization of the cytoskeleton and its pivotal role in cellular motility, intracellular transport, and structural integrity .
-
Factory overhead of $44,700 consists of Indirect labor of $21,900, Depreciation expense-Factory of $16,900, and Factory utilities of $5,900. a. Compute total manufacturing costs. b. Prepare a...
-
Marc, a single taxpayer, earns $ 6 0 , 0 0 0 in taxable income and $ 5 , 0 0 0 in interest from an investment in city of Birmingham bonds. Using the U . S . tax rate schedule for year 2 0 2 3 , what...
-
On the first day of the fiscal year, a company issues a $990,000, 8%, 5-year bond that pays semiannual interest of $39,600 ($990,000 x 8% x 1/2), receiving cash of $884,176. Journalize the entry for...
-
Name all the alcohols that have the formula C5H12O. How many ethers have the formula C5H12O?
-
Define deferred revenue. Why is it a liability?
-
Explain which transportation mode would probably be most suitable for shipping the following goods to a large Los Angeles department store: a. 300 pounds of Maine lobster. b. 15 pounds of...
-
Indicate the nearest location where you would expect to find large storage facilities. What kinds of products would be stored there? Why are they stored there instead of some other place?
-
When would a producer or intermediary find it desirable to use a public warehouse rather than a private warehouse? Illustrate, using a specific product or situation.
-
Respond to two colleagues: Describe one way each colleague might assist a client in late adulthood with midlife adjustment and well-being to address the factors she or he described. Describe two...
-
Consider the South African retail banking sector in general - What are the core capabilities and resources needed to be successful in the South African retail banking sector? Identify and discuss at...
-
"Corporate Social Responsibility: a business philosophy which stresses the need for firms to behave as good corporate citizens, not merely obeying the law but conducting their production and...
Study smarter with the SolutionInn App