--%>
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 : 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 : MANOVA and Reflection Activity 10:

    Activity 10: MANOVA and Reflection 4Comparison of Multiple Outcome Variables This activity introduces you to a very common technique - MANOVA. MANOVA is simply an extension of an ANOVA and allows for the comparison of multiple outcome variables (again, a very common situation in research a

    		•
  • 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 : Probability Distributions and Data

    1. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approxi

    		•
  • Q : Non-parametric test what is the

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

    		•
  • 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 : Describe what happens to the confidence

     A nurse practitioner working in a dermatology clinic is studying the efficacy of tretinoin in treating women's post partum abdominal stretch marks.  From a sample of 15 women, the mean reduction of stretch mark score is -0.33 with a sample standard deviation of 2.46.  Describe wha

    		•
  • 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 : Problem related to playing cards Cards

    Cards are randomly drawn one at the time and with replacement from a standard deck of 52 playing cards. (a) Find the probability of getting the fourth spades on the 10th draw. (b) Determine the

    		•