Solve the statistics below

How many chords can be drawn through 21 points on a circle?

4. How many triangles can be formed by joining the vertices of a hexagon?

5. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels

can be formed?

6. If four dice are rolled, find the number of possible outcomes in which atleast one

die shows 2.

7. There are 18 guests at a dinner party. They have to sit 9 guests on either side of

a long table, three particular persons decide to sit on one particular side and two

others on the other side. In how many ways can the guests to be seated?

8. If a polygon has 44 diagonals, find the number of its sides.

9. In how many ways can a cricket team of 11 players be chosen out of a batch of 15

players?

(i) There is no restriction on the selection.

(ii) A particular player is always chosen.

(iii) A particular player is never chosen.

10. A Committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this

can be done when

(i) atleast two ladies are included

(ii) atmost two ladies are include

The retailer's new Chief Executive Officer, Mr Julius Kipng'etich, said the

organization's board had chosen to shut down local units to accelerate the way toward settling its Kenyan activities.

Preceding shutting down, the board employed the administrations of P WC to direct a legal review on Uchumi monetary and operational perfortnance basing on accessible auxiliary information and some semi-organized with key stafT. The discoveries?itnplyexacerbated the nnger_of investors. The inspectors

2 found that, notwithstanding fit compensations, top and ntiddle administrators were given gigantic monetary rewards paying little mind to their perfortnance. tnean yearly reward for all top chiefs was Shs. 500,000,000.

The mean yearly reward paid to top leaders was Shs. 520,000,000 while mean yearly rewards paid to center leaders was Shs. 420,000,000.

In Uganda, the grocery store monster had branches in Kampala and Gulu. After the conclusion, leasers struck all branches dernanding a total settlement of unfulfilled obligations else they drag the once store

3 goliath to court. The board concurred that for sure there are numerous lenders yet mentioned PWC to stretch out its to incorporate the quantity of leasers per locale, normal extraordinary sums and conceivable change in such remarkable settletnents.

Gulu branch Kam ala Branch

Number of loan bosses 50 100 Average credit sum 120 85

Fluctuation in credit sums 9 16

{EQUIRED

a) Suggest and clarify any three advantages of utilizing the information gathering technique featured in the second section of the case (6 Marks)

b) Using the standard of consolidated mean for two conveyances, decide the level of top and center chiefs who were utilized by Uchumi Supermarket (10 Marks)

c) By utilizing the rule of Coefficient of Variation, which of the two branches in Uganda showed more consistency in credit sums? (5 Marks)

d) While figuring the normal and change in credit sums for the Kampala branch, the inspector from P WC unintentionally caught one of the acknowledge sums as 120 rather than the right 100 million as demonstrated on the provider receipt. By utilizing the rule of changing the right mean from an off-base mean, re-figure the right fluctuation in credit sums. (12 Marks)

ollowing information demonstrates month to month pay rates of representatives inside KCCA

20.75 21.28 22.02 22.51 22.55 23.75 24.03 24.24 25.17 25.19 25.7 25.91

26.13 26.32 26.33 27.01 27.13 27.55 27.57 27.79 28.17 30.46. 30.9

) Extract a comprehensive recurrence appropriation of five classes beginning with 19.55 ? 21.82, 21.83?24 etc.... (6 Marks)

Register the Coefficient of Variation and remark on the appropriation of the informational collection (11 Marks)

End of test

Problem 1 (20 points): Consider a sample space S consisting of a countable number of outcomes. Suppose that a probability function P has been defined that satisfies the three Axioms of Probability. Let E be an event with non-zero probability, so that P(E) > 0. For an arbitrary event F, consider the conditional probability defined as P(FIE) = P(FE)P(E). Prove that the conditional probability is also a probability. That is, prove that it satisfies the Axioms of Probability. Show all work. Prove every step unless it is obvious (even then a reason is recommended).. Quartiles . Variance and standard deviation-Focus on understanding what they are trying to mea . Sample space . Events, simple events, compound events . Set notation for complements, intersections, and unions . Disjoint events . Basic probability axioms such as P(S) = 1 and P(A) 2 0. . Probability of complement events: P(A) + P(A') = 1 . Probability of P(A U B) . Probability of P(AUBUC) . Counting techniques-permutations and combinations . Hypergeometric probabilities . Conditional probability P(A|B) . Probability of P(An B) . Independent events . Random Variables-Discrete vs. Continuous . Probability distributions or probability mass functions for dry (discrete random variable . Cumulative distribution functions for dry and how to graph them . Expected Values for a dry X (i.e. given a probability distribution of a dry X, E(X) =.. . The Expected Value of a Function of a dry-given h(X), find E(h(X)). . The Variance of a dry X and the standard deviation1.3 Bounds on probabilities [15 points] Two events Al and A2 in a sample space 2 are such that P(A1 ) = 0.3 and P(A2) = 0.5. a) Is it possible that A1 and A2 are exhaustive? b) Is it possible that P(A1 OR A2) = 0.9? Why? Can you show it using the axioms of probability? c) Is it possible that P(A] AND A2) = 0.4. Why? Can you show it using the axioms of probability