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Assignment

Name: Naeem Sajjad

Registration ID 056

Course Name Quantitative Business Analysis

Course Code M ! 6"#

$rogram %MBA &'5(

Semester )all

Date o) Su*mission +5,&0,+0&5

8/18/2019 Question for a successful job interview

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Question 1

Consider an experiment which consists of 2 independent coin tosses. Let therandom variable x denotes the number of heads appearing. What is theprobability of?

robability of 1 head appearing

robability of 2 head appearing

The four outcomes are equally likely in this case so the probability is ¼. But ingiven experiment 2 coins tosses are independent

1. Probability of 1 head appearing1!"#1!" $ 1!2

2. Probability of 1 head appearing%o it is the product of P &'( and P &'( )hich is1!2 #1!2 $ 1!"

The four possible outcomes can be classified in terms of the number of heads thatcome up. The number could be t)o &*utcome 1(+ one &*utcomes 2 and ,( or -&*utcome "(.

!umber of heads

robability

- 1!"1 1!2

, 1!"

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Question 2

!ormal "istribution#

The normal distribution is one of important class of statistical distribution thiskind of data distribution can be seen in many natural phenomenon such as height+lengths of ob/ects manufactured by machines+ marks on test+ errors in measurementand blood pressure. 0ll normal distributions are symmetric and have bell shapeddensity curves )ith a single peak. n normal distribution t)o quantities nee to bespecified the mean &peak of density occurs( and the standard deviation &girth of

bell curve(.

The spread of a normal distribution is controlled by the standard deviation & σ (+ thesmaller the standard deviation the more concentrated the data. 0nd the mean andthe median are the same in a normal distribution.

Characteristics and uses ma$e difference in binomial and naturaldistribution#

The follo)ing are characteristics of normal distribution

• 3ean $ 3edian$ 3ode• %ymmetrical to the centre+ no bias left or right.• 4-5 values are less than mean and 4-5 are more than mean

"ifference

1. Binomial distribution is very much different from normal distribution. But if the sample si6e is large then shapes of histograms )ill be quite similar.

2. The main difference is that binomial distribution is discrete not continuouslike normal distribution. 7hich means that it not possible to find a datavalue bet)een any t)o variables in binomial distribution+ but in normaldistribution )e can do so.

3. 8ormal distribution arises in natural process such as height+ sampling process and repeated measurements of a fixed phenomenon such as orbitalmovement of mars in contrast binomial distribution arises )hen r.v of interest is the count of successes in a fixed number of trials.