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






  • 100% Plagiarism-Free Guarantee

    We deliver top-quality essays through employing various measures that seek to improve the content of a given assignment. One of the quality-control systems that we use entails plagiarism checkers. These systems help us to deliver a 100% plagiarism-free papers to our clients. We also value the originality of papers, and we do not resell any submitted paper. It means that every client always gets a unique paper. Additionally, our perfect team of writers is usually keen on the academic writing standards as well as the instructions brief that a client submits. Our team of writers holds matchless competence when it comes to its service delivery. Every member of the team usually has an academic degree, and the team’s diversified skills make it possible for us to have a qualified writer in any client’s area of study. Additionally, our past clients have always given a positive feedback on each of our writers.

  • Free Revisions

    The papers that we deliver usually reflect a high quality level. However, there is always a room for any additional fine-tuning touch in line with a client’s preference without any additional charges. To begin with, a client has discretion to make a choice on their preferred top writer from our team. Such a writer could have handled past work for the client and received a positive review from the same. It means that the client has confidence of the quality of service that the writer delivers. Secondly, a client has an option of making use of our editing services. Our editors are always on standby to revise the paper and ensure that it matches with the expectations of a client that the instruction brief had detailed. The revision covers content adjustment that removes off-topic details, addition of sources, removal of language style errors, and assessment of the referencing style in order to enhance compliance.

  • 100% Confidentiality

    We mind about the interests of our clients holistically. It is for this reason that we maintain high-level confidentiality in regard to our clients’ personal information. Importantly, we use the information for purposes that relate with our services only. The only information that we require relates to our clients’ writing needs. It is also important to note that our clients’ payment information is secure with us. If there is any query in regard to the payment information, then our support team is always willing to provide any clarifications in a prompt manner. Confidentiality extends to the fact that a client made use of our services. It means that we hold our relationship with our clients in secrecy. Importantly, our confidentiality measures beat any advanced security measure that can identify any information regarding our relationship with our clients. It means that our clients transact with us freely without any fear of information leakage.

  • 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.




Related Questions