Let X1, X2,... be nonnegative i.i.d. random variables with E(X) = 3 and Var(Xk) = 1. (a) (2 points) Use Markov's inequality to give an upper bound on P(X1> 5). (b) (2 points) Use Chebyshev's inequality to estimate P(|X1 – 3| > 2). (c) (5 points) Give a number n so that X1+.+Xn P(|조i++Xn _3|> 2) < 10. n Briefly justify your answer.

Let X1, X2,... be nonnegative i.i.d. random variables with E(X) = 3 and Var(Xk) = 1. (a) (2 points) Use Markov's inequality to give an upper bound on P(X1> 5). (b) (2 points) Use Chebyshev's inequality to estimate P(|X1 – 3| > 2). (c) (5 points) Give a number n so that X1+.+Xn P(|조i++Xn _3|> 2) < 10. n Briefly justify your answer.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

I need help with this please
What sort of information would you collect with probability
Let’s assume the odds of getting a disease indoors in a classroom is 15%. In a class of 28 students, what is the probability that… Question #4: Half of the students get the disease?
At races, your horse, White Rum, has a probability of 1/20 of coming 1st, 1/10 of coming 2nd and a probability of ¼ in coming 3rd. First place pays $5,000 to the winner, second place $4,000 and third place $1,350. Hence, is it worth entering the race if it costs $1050?
I need help with this attached question, please. The parts a to c are: (a) Find the probability that a married couple watches the show. (b) a wife watches the show, given that her husbanddoes; (c) at least one member of a married couple will watchthe show.
Are there any restrictions on the value of a probability? If so, explain what those restrictions are.
The below was the answer I received when I asked the following question. Dr. Deming’s Red Bead Experiment is an exercise in the laws of probability. The workers were frustrated because no matter what they did, the outcome was not predictable. If the paddle holds 50 beads and there are 500 white beads and 50 red beads in the box, what is the probability, using one sample, of filling a paddle with 47 white beads and only three red beads? What I need to understand is how did you get the highlighed answers below because these require a factorial of 500 and I have not found anything that will calculate that. Thank you Step 1 Given Information: Number of white beads = 500 Number of red beads = 50 Total number of beads = 550 Step 2 The probability, using one sample, of filling a paddle with 47 white beads and only three red beads can be determined as follows: Probability = C47500*C350C50550=(2.94*10^66) (19600)(3.44*10^71)=0.1675
Consider the joint pmf p(x,y) and marginal pmfs p(x) and p(y) for two discrete random variables X and Y as displayed in the table below. X p(x,y) 1 2 3 p(y) 1 0.125 0.0625 0.1875 0.125 0.5 Y 2 0.0625 0.0625 0.125 0.25 0.5 p(x) 0.1875 0.125 0.3125 0.375 1
Hello! I need help with following probability problem. Thank you in advance..!