--%>
Assignment Help - homework help

Probability of Rolling die problem

A fair die is rolled (independently) 12 times.

(a) Let X denote the total number of 1’s in 12 rolls. Find the expected value and variance of X.

(b) Determine the probability of obtaining exactly four 1’s.

(c) Determine the probability of obtaining at least one 1.

(d) Approximate the probability in part (b) using Poisson approximation to binomial distribution. What is the percent relative error of approximation (round the answer off to two decimal places)?

(e) Approximate the probability in part (c) using Poisson approximation to binomial distribution. What is the percent relative error of approximation (round the answer off to two decimal places)?

   Related Questions in Advanced Statistics

  • Q : Problem on Chebyshevs theorem 1. Prove

    1. Prove that the law of iterated expectations for continuous random variables.2. Prove that the bounds in Chebyshev's theorem cannot be improved upon. I.e., provide a distribution which satisfies the bounds exactly for k ≥1, show that it satisfies the

    		•
  • Q : Problem on layout A manufacturing

    A manufacturing facility consists of five departments, 1, 2, 3, 4, and 5. It produces four components having manufacturing product routings and production volumes indicated below.   1. Generate the from-to matrix and the interaction matrix. Use a

    		•
  • Q : Calculate corresponding t value or s

    1)    Construct a 99% confidence interval for the population mean µ.   2)    At what significance level do the data provide good evidence that the average body temperature is

    		•
  • Q : Use the law of iterated expectation to

    Suppose we have a stick of length L. We break it once at some point X _

    Q : Problem on consumers marginal utility

    Consider a consumer with probability p of becoming sick.  Let Is be the consumer’s income if he becomes sick, and let Ins be his income if he does not become sick, with Is < Ins. Suppo

    		•
  • Q : Frequency Distributions Define the term

    Define the term Frequency Distributions?

    		•
  • Q : Analysing the Probabilities 1. In the

    1. In the waning seconds of Superbowl XLVII, the Baltimore Ravens elected to take a safety rather than punt the ball. A sports statistician wishes to analyze the effect this decision had on the probability of winning the game. (a) Which two of the following probabilities would most help t

    		•
  • Q : Probability of winning game Monte Carlo

    Monte Carlo Simulation for Determining Probabilities 1. Determining the probability of winning at the game of craps is difficult to solve analytically. We will assume you are playing the `Pass Line.'  So here is how the game is played: The shooter rolls a pair of

    		•
  • Q : Non-parametric test what is the

    what is the appropriate non-parametric counterpart for the independent sample t test?

    		•
  • Q : Grouped Frequency Distributions Grouped

    Grouped Frequency Distributions: Guidelines for classes: A) There must be between 5 to 20 classes. B) The class width must be an odd number. This will assure that the class mid-points are integers rather than decimals. C) The classes should be mutually exclusive. This signifies that no data valu

    		•