Use the following to answer questions 1 - 4: Suppose a pdf of X is defined by the function1. What is the probability of ...

Get help with any kind of assignment - from a high school essay to a PhD dissertation

  1. Order Custom Essay, Course Work, Research and Term Papers

MATH 3339-What is the probability of X

April 14, 2018

Use the following to answer questions 1 - 4: Suppose a pdf of X is defined by the function

1. What is the probability of X < 0.3?
a. 0.3
b. 0.75
c. 0.25
d. 0.5
e. 0.12
2. Determine the probability P(0.275 ? X ? 0.35).
a. 0.075
b. 0.1875
c. 0.8125
d. 0.1375
e. 0.8625
3. Give the first quartile (Q1) of X.
a. 0.25
b. 0.1
c. 2.5
d. 0.3
e. 0.2
4. Find the median of the density curve.
a. 1
b. 0.2
c. 2.5
d. 0.4
e. none of these

For problem 5 - 7, let X have the following pdf.

5.Determine the value of k.
a. 0
b. 1
c. 2
d. 3
e. 0.5

6. Determine the mean of X.
a. 1.5
b. 2.25
c. 3
d. 1.25
e. None of these above.
7. Determine the variance of X.
a. 2.25
b. 5.4
c. 0.3375
d. 0.581
e. None of these above.
Use the following to answer questions 8 - 11. Suppose that a random variable X has a cdf of

8. What is the probability P(X < 0)?
a. 1/9
b. 1/12
c. 2/9
d. 0
e. None of these above.
9. What is the probabiltiy P(0 < X ? 1)?
a. 0.1111
b. 0
c. 0.1389
d. 0.5000
e. None of these above.
10. Find the value of c such that P(X ? c) = 0.1.
a. -0.4642
b. 0.1
c. 1.282
d. 1.922
e. -1.282
11. Determine E[X].
a. 1.5183
b. 1.25
c. 1.50
d. 0
e. None of these above.

12. *Let X denote the amount of time for which a book on 2-hour reserve at a college library is
checked out by a randomly selected student and suppose that X has density function:

Calculate the following probabilities:
a. P(X ? 1)
b. P(0.5 ? X ? 1.5)
c. P(1.5 < X)
13. **The cdf of checkout duration X as described in the previous exercise is

Use this to compute the following:
a. P(X ? 1)
b. P(0.5 ? X ? 1.5)
c. P(1.5 < X)
d. Determine the median checkout duration. That is find x such that F(x) = 0.5.
e. Compute F’(x) to obtain the density function f(x).
14. ***Reconsider the distribution of checkout duration X described in the previous two
problems. Compute the following:

a. E(X)
b. If the borrower is charged an amount h(X) = X2 when checkout duration is X,
compute the expected charge E[h(X)].
c. V(X) and SD(X).
15. For 0 ? x ? 1 let f(x) = kx(1 ? x), where k is a constant.
a. Find the value of k such that f is a density function.
b. Find the cumulative distribution for the previous density function.
16. Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform
distribution by X ~ Unif(-5, 5).

a.
b.
c.
d.

Give the pdf of X.
Compute P(X < 0).
Compute P(-2.5 < X < 2.5)
For k satisfying -5 < k < k +4 < 5, compute P(k < X < k +4).

17. Suppose jobs arrive every 15 seconds on average, ? = 4 per minute, has an exponential
distribution.

a. What is the probability of waiting less than or equal to 30 seconds, i.e .5 min?
b. Compute E(X).
c. Compute Var(X) and SD(X).










OUR SERVICE CHARTER






  • Money Back Guarantee

    If any of our writers deliver an incomplete or ambiguous paper that is off the topic, our clients can claim for a refund in regard to the oversight. We do not compromise our service delivery through submission of a paper that does not follow our clients’ instructions. We also mind about the interest of our customers, and we always give them value for their money. However, our clients have a choice to request for a free revision within 14-30 days, or depending on the length of the submitted paper. A client who needs a refund should send a request for it within 14 days after receiving the completed paper. If a client decides not to download the paper, then they can request for 100% refund. Any refunded amount usually goes to the client’s Bonus Balance as store credit. There is always extra compensation when the refund takes the form of store credit. Alternatively, the refunded amount can also go the client’s credit card.

  • Better Grades Guarantee

    Our team of writers prides in high-level competence. The writers have the required expertise that enables them to deliver quality papers that match with the requirements of the grading rubric. In the absence of the rubric, we ensure that the writers follow the clients’ instruction brief to the letter. We can confidently assure our clients to expect nothing short of a pass from the papers that we deliver. Importantly, we have qualified writers who handle different areas of study. This diversification enables us to allot clients’ orders to the writer who is well seasoned in the subject area of study. It also enables the team to become more professional due to specialization. Our clients should put their trust in our service delivery and expect to successfully attain high grades at all times. The fact that we offer free revision reflects our dedication in delivering high quality papers that match with our clients’ expectations.

  • 24/7 Customer Support

    Our team of writers prides in high-level competence. The writers have the required expertise that enables them to deliver quality papers that match with the requirements of the grading rubric. In the absence of the rubric, we ensure that the writers follow the clients’ instruction brief to the letter. We can confidently assure our clients to expect nothing short of a pass from the papers that we deliver. Importantly, we have qualified writers who handle different areas of study. This diversification enables us to allot clients’ orders to the writer who is well seasoned in the subject area of study. It also enables the team to become more professional due to specialization. Our clients should put their trust in our service delivery and expect to successfully attain high grades at all times. The fact that we offer free revision reflects our dedication in delivering high quality papers that match with our clients’ expectations.

  • Excellent Quality Work

    Grammar is one of the elements that we take seriously in our service delivery. Beside the use of spell checkers, we progressively take our writers through the essentials of a quality paper that features information clarity. Importantly, we encourage our writers to avoid coming up with a paper that deviates from the elements that appear on the client’s instruction brief. It means that the papers that we deliver denote well researched information that is rich in details. Additionally, the papers usually contain exhaustive details on any instruction that a client submitted. It is the tireless application of our writers’ efforts that makes us stand out when it comes to the delivery of excellent quality work. Notably, our writers use quality resources when digging up information that a paper requires. They are usually aware of the sources that contain rich information. Our past clients have proved that we give nothing short of quality work through giving us a positive feedback.




Related Questions