**QUESTION 1.**

**(a). **The random variable X is the number of siblings of a student selected at random from Professor Appiah’s Introductory Statistics class. It’s probability distribution is given in the following table.

x |
0 |
1 |
2 |
3 |
4 |
5 |

P(X=x) |
1/4 |
1/3 |
1/6 |
7/48 |
1/16 |
1/24 |

Find the following

(i). The expected value of the random variable X. **(3 points)**

(ii).The standard deviation of the random variable X.** (5 points)**

(iii).The variance of the random variable X.** (2 points) **

**(b).**Let Y represent the number of Boys in families having three children.

(i). List all possible birth order permutations for families having three children and give the value of Y for each outcome and their associated probabilities.** (5 points) **

[**Hint**: a family ofthree is made up of Boys and Girls]. Use your probability distribution to find the following

(i). The mean of the random variable Y.** (3 points)**

(ii).The standard deviation of the random variable Y.** (5 points)**

(iii). The variance of the random variable Y.** (2 points) **

** **

**QUESTION 2.**

A die is altered by painting an additional dot on the face that originally had one dot. A pair of such altered dice is rolled.

**(a).**(i).** **Make a table for the sample space of the outcome of this experiment.

**(4 points)**

(ii).If X is the sum of the number of dots showing on both dice together, what are the possible values of X.**(3 points).**

**(b).**(i). Calculate the probabilities ofthe possible values of X from **a(ii)**.** (4 points) **

(ii).Make a table for the probability distribution of X and verify it is a valid one.

**(4 points) **

**(c).**(i). Find E[X(X-1)]. **(5 points)**

(ii).Find the variance (Var[X]) and the standard deviation (SD[X]). **(5 points)**

** **

**QUESTION 3.**

** (a).**On a multiple choice test of 13 questions, each question has four (4) possible answers, one of which is correct. For students who guess at all answers, find the following if X is the number of correct answers.

(i). The mean of the random variable X. **(2 points)**

(ii). The standard deviation of the random variable X.** (2 points) **

**(b). **Given that the probability function p(x)=(7-x)/12 for x=1,2,3 4 and 5. Find P(1),P(2), P(3), P(4), and P(5).** (5 points) **

**(c).**In a city the probability that a person will pass his or her driving test the first attempt is 0.66.Four people are selected at random from among those taking their driving test for the first time. Determine the following.

(i). The probability that exactly one person passed the test. **(3 points)**

(ii). The probability that exactly two persons passed the test. **(3 points)**

(iii) The probability that at least two persons passed the test. **(5 points)**

(iv). The probability that at least three persons passed the test. **(5 points)**

** **

**QUESTION 4.**

**(a).**Suppose X has a Poisson distribution with parameter λ=11.44. Find the following.

(i). The mean of X**. (2 points).**

(ii).The standard deviation of X. **(2 points).**

**(b).**The number of lightning strikes in a year at the top of particular mountain has a Poisson distribution with parameterλ=2.9.Find the following.

(i). The probability that in a randomly selected year the number of striking is less than or equal to 5.**(5 points)**

(ii). The probability that in a randomly selected year the number of striking is greater than 5.** (3 points)**

**(c).**The probability that a call received by a certain switchboard will be a wrong number is 1 per 100 calls. Use Poisson approximation to the binomial distribution to find the probability that among 120 calls received by the switchboard,

(i).There are no wrong numbers. **(2 points)**

(ii).There is exactly one wrong number. **(2 points)**

(iii). There are exactly two wrong numbers. **(2 points)**

(iv). There are exactly three wrong numbers. **(3 points)**

(v). There are at most three wrong numbers. **(4 points)**

**Note:** This Homework covers material on section D. Please be advised that you are supposed to follow all the necessary steps and procedures to enable you arrive at the final answer. Don’t just give me the answers because mathematics is not just about answer; it is about how you arrived at the answers. This Homework per say is not difficult, but if you don’t follow the steps you will not end up getting the full credit. Thank you for your co-operation and understanding.

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more
## Recent Comments