--%>
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 : Components of time series Name and

    Name and elaborate the four components of time series in brief.

    		•
  • 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 : Probability and Statistics

    Instructions: Do your work on this question and answer sheet. Please print or write legibly, and, as always, be complete but succinct. Record your answer and your supporting work in the designated space. Explain your method of solution and be sure to label clearly any

    		•
  • 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 : Describe how random sampling serves

    Explain sampling bias and describe how random sampling serves to avoid bias in the process of data collection.    

    		•
  • Q : Variation what are the advantages and

    what are the advantages and disadvantages of seasonal variation

    		•
  • Q : Error probability As of last year, only

    As of last year, only 20% of the employees in an organization used public transportation to commute to and from work. To determine if a recent campaign encouraging the use of public transportation has been effective, a random sample of 25 employees is to be interviewe

    		•
  • Q : Pearsons correlation coefficient The

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

    		•
  • 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 : Analyse the statistics of the data

    Assigment Question Select any two manufacturing companies and formulate the cost and revenue functions of the companies. analyse the statistics of the data and then sketch the functions and determine their breakeven points. (Note: You are required to interview the production and sales manag

    		•