--%>
Assignment Help - homework help

Find the cumulative distribution function

You must use the pre-formatted cover sheet when you hand in the assignment.

Out full detailed solutions. Sloppy work will naturally receive a lower score.

1. Suppose at each step, a particle moving on sites labelled by integer has three choices: move one site to the right with probability p (where 0 ≤ p ≤  1/2 ), move one site to the left with probability 1 - 2p or stay where it is with probability p.

370_market.png

 

The particle starts at position 0 and moves two steps.

(a) Let f(p) be the probability that the particle is at position 0 after moving two steps. Find f(p) in terms of p and evaluate the expression (correct to 2 decimal places) when p = 0:3.

(b) Let g(p) be the probability that the particle is one site away from position 0 after making two steps (positions +1 and -1 both qualify as being one site away from position 0). Find g(p) in terms of p and evaluate the expression (correct to 2 decimal places) when p = 0:3.

(c) Let h(p) be the probability that the particle is two sites away from position 0 after making two steps. Find h(p) in terms of p and evaluate the expression (correct to 2 decimal places) when p = 0:3. 

(d) Find the value of p that minimizes f(p). 

(e) Find the value of p that maximizes g(p).

2. The continuous random variable X has cdf (cumulative distribution function) given by

401_market2.png

(a) Find the value of k. 

(b) Find E(X). 

(c) Find the median of X. 

(d) Find the standard deviation of X, correct to 2 decimal places.

(e) Denoting E(X) by μ and the standard deviation of X by , nd P(X < (σ)).

3. The velocity V of a moving object has a probability density function (pdf) shown in the diagram:

462_market1.png

(a) Find the cumulative distribution function (cdf) of V . 

(b) In Physics, we know that the relationship between kinetic energy K and the ve- locity V of a moving object with mass m (m is xed in this question) is:

K = 1/2mV2

If V has pdf as given in the diagram above, nd the pdf of K. 

 

 

 

 

 

 

 

 

   Related Questions in Advanced Statistics

  • Q : What is your statistical decision

    Question 1 Do parents with more children travel more than parents of small families? To find out, a survey was done of a large number of adults. Respondents were asked how many children they had and how many times

    		•
  • Q : Analytical Report Hi I WOULD LIKE TO

    Hi I WOULD LIKE TO KNOW IF YOU CAN HELP ME TO DO THE ASSIGNMENT IN HEALTH STATISTICS THANKS

    		•
  • Q : Frequency Distributions Define the term

    Define the term Frequency Distributions?

    		•
  • Q : Null hypothesis In testing the null

    In testing the null hypothesis H0: P=0.6 vs the alternative H1 : P < 0.6 for a binomial model b(n,p), the rejection region of a test has the structure X ≤ c, where X is the number of successes in n trials. For each of the following tests, d

    		•
  • Q : Probability of Rolling die problem A

    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 e

    		•
  • Q : True and False Statement Discuss the

    Discuss the following statements and explain why they are true or false: a)      Increasing the number of predictor variables will never decrease the R2 b)      Multicollinearity affects the int

    		•
  • 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 : Conclusion using p-value and critical

    A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evid

    		•
  • 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 : Variation what are the advantages and

    what are the advantages and disadvantages of seasonal variation

    		•