--%>
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 : Variation what are the advantages and

    what are the advantages and disadvantages of seasonal variation

    		•
  • 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 : Calculate confidence interval A nurse

    A nurse anesthetist was experimenting with the use of nitronox as an anesthetic in the treatment of children's fractures of the arm.  She treated 50 children and found that the mean treatment time (in minutes) was 26.26 minutes with a sample standard deviation of

    		•
  • Q : Pearsons correlation coefficient The

    The table below illustrates the relationship between two variable X and Y. A

    		•
  • 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 utility funtion probability

    Suppose that your utility, U, is a function only of wealth, Y, and that U(Y) is as drawn below. In this graph, note that U(Y) increases linearly between points a and b.  Suppose further that you do not know whether or not you

    		•
  • Q : Probability problem A) What is the

    A) What is the probability of getting the following sequence with a fair die (as in dice):B) What is the probability of getting the same sequence with a die that is biased in the following way: p(1)=p(2)=p(3)=p(4)=15%;

    		•
  • 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

    		•
  • Q : Random variables Random variables with

    Random variables with zero correlation are not necessarily independent. Give a simple example.    

    		•