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18 August Maths


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18 August Maths

  2. 2. THEORETICAL DISTRIBUTIONS IN BUSINESS STATISTICS Dr. T.K. Jain. AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email_address] ,
  3. 3. X is a binomial distribution, with N = 20. If it is symmetric, what is Mean? <ul><li>Mean = NP </li></ul><ul><li>It is symmetric, therefore P = ½ </li></ul><ul><li>Thus mean = 20 * ½ = 10 answer. </li></ul>
  4. 4. N = 16, then what will be the maximum value of variance of X, (binomial distribution)? <ul><li>Variance = NPQ </li></ul><ul><li>The maximum variance will possible if P = ½ and Q = ½ </li></ul><ul><li>16*1/2*1/2 = 4 answer. </li></ul>
  5. 5. What is the mean of chi-square distribution? <ul><li>N </li></ul>
  6. 6. What is the standard deviation of chi-square distribution? <ul><li>Sqrt( 2n) </li></ul>
  7. 7. What is the mean deviation of normal distribution? <ul><li>.8 σ </li></ul>
  8. 8. What are first and 3 rd quartiles in normal distribution? <ul><li>μ + .675 σ </li></ul><ul><li>μ - .675 σ </li></ul>
  9. 9. What is biparametric distribution? <ul><li>Normal distribution, because there are 2 parameters – </li></ul><ul><li>1. μ (mu or population mean) </li></ul><ul><li>2. σ ^2 or (variance of population). </li></ul><ul><li>If these 2 parameters are known, normal distribution can be specified. </li></ul>
  10. 10. What is the area from ∞ to 0? <ul><li>.5 </li></ul>
  11. 11. What is the area from 0 to ∞? <ul><li>.5 answer. </li></ul>
  12. 12. What is probability density function of normal distribution? <ul><li>[1/ { σ sqrt(2pi)} ]*e^(n- μ )/2 μ ^2 </li></ul>
  13. 13. What is the mean of t distribution? <ul><li>Zero </li></ul>
  14. 14. What is the standard deviation of t distribution? <ul><li>Sqrt (n/n-2) </li></ul>
  15. 15. When is t distribution similar to normal distribution? <ul><li>When N is more than 30. (large sample). </li></ul>
  16. 16. What is mean of F distribution? <ul><li>N2 / (N2-2) </li></ul>
  17. 17. What is standard deviation of F distribution? <ul><li>N2/n2-2 * sqrt ((2(n1+n2 – 2))/n1(n2-4)) </li></ul><ul><li>N2 must be more than 4. </li></ul>
  18. 18. What type of skewness is there in F distribution? <ul><li>Positive skewness. </li></ul>
  19. 19. Does a theoretical distribution exist? <ul><li>Does not exist </li></ul>
  20. 20. Mention a discrete probability distribution? <ul><li>Poisson distribution </li></ul><ul><li>(normal distribution is a continuous distribution). </li></ul>
  21. 21. Parameter is a characteristic of ? <ul><li>Population </li></ul><ul><li>(statistics is for sample characteristics) </li></ul>
  22. 22. What are parameters? <ul><li>Characteristics of population, example: </li></ul><ul><li>Mean, standard deviation, etc. </li></ul>
  23. 23. Is binomial distribution symmetrical? <ul><li>Yes but only when P = .5, otherwise not </li></ul>
  24. 24. When are mean, mode and median equal? <ul><li>When a distribution is symmetrical </li></ul>
  25. 25. What is the variance of binomial distribution? <ul><li>NPQ </li></ul>
  26. 26. 1.5% production is defective. If we take a sample of 200, what is the probability that it will contain Zero defectives? <ul><li>NCRP^r*Q^(n-r) </li></ul><ul><li>=200C0 * (.015)^0*(.985)^200 </li></ul><ul><li>=.048 answer. </li></ul>
  27. 27. What is the probability of getting 3 correct answers in 5 true false type questions? <ul><li>NCRP^r*Q^(n-r) </li></ul><ul><li>= 5C3*(1/2)^3*(1/2)^2 </li></ul><ul><li>=.3125 answr. </li></ul>
  28. 28. Overall probability of passing is 50%, what is the probability that out of 10 students in our class, at least 9 will pass? <ul><li>NCRP^r*Q^(n-r) </li></ul><ul><li>10C9(.5)^9*(.5)^1 = .01 </li></ul><ul><li>+10C10(.5)^10*(.5)^0 = .0009 </li></ul><ul><li>=.0109 answer. </li></ul>
  29. 29. Quartile deviation of a normal curve is 4.05, what is its mean distribution? <ul><li>.675 σ = 4.05 </li></ul><ul><li>.8 σ = 4.05/.675*.8 = 4.8 answer. </li></ul>
  30. 30. ABOUT AFTERSCHO☺OL <ul><li>Afterschoool conducts three year integrated PGPSE (after class 12 th along with IAS / CA / CS ) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM . This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society. </li></ul>
  31. 31. Why such a programme? <ul><li>To promote people to take up entrepreneurship and help develop the society </li></ul><ul><li>To enable people to take up franchising and other such options to start a business / social development project </li></ul><ul><li>To enable people to take up social development as their mission </li></ul><ul><li>To enable people to promote spirituality and positive thinking in the world </li></ul>
  32. 32. Who are our supporters? <ul><li>Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us. </li></ul><ul><li>You can also support us – not necessarily by money – but by being promotor of our concept and our ideas. </li></ul>
  33. 33. About AFTERSCHO☺OL PGPSE – the best programme for developing great entrepreneurs <ul><li>Most flexible, adaptive but rigorous programme </li></ul><ul><li>Available in distance learning mode </li></ul><ul><li>Case study focused- latest cases </li></ul><ul><li>Industry oriented practical curriculum </li></ul><ul><li>Designed to make you entrepreneurs – not just an employee </li></ul><ul><li>Option to take up part time job – so earn while you learn </li></ul><ul><li>The only absolutely free course on internet </li></ul>
  34. 34. Workshops from AFTERSCHO☺OL <ul><li>IIF, Delhi </li></ul><ul><li>CIPS, Jaipur </li></ul><ul><li>ICSI Hyderabad Branch </li></ul><ul><li>Gyan Vihar, Jaipur </li></ul><ul><li>Apex Institute of Management, Jaipur </li></ul><ul><li>Aravali Institute of Management, Jodhpur </li></ul><ul><li>Xavier Institute of Management, Bhubaneshwar </li></ul><ul><li>Pacific Institute, Udaipur </li></ul><ul><li>Engineering College, Hyderabad </li></ul>
  35. 35. Flexible Specialisations: <ul><li>Spiritualising business and society </li></ul><ul><li>Rural development and transformation </li></ul><ul><li>HRD and Education, Social Development </li></ul><ul><li>NGO and voluntary work </li></ul><ul><li>Investment analysis,microfinance and inclusion </li></ul><ul><li>Retail sector, BPO, KPO </li></ul><ul><li>Accounting & Information system (with CA / CS /CMA) </li></ul><ul><li>Hospital management and Health care </li></ul><ul><li>Hospitality sector and culture and heritage </li></ul><ul><li>Other sectors of high growth, high technology and social relevance </li></ul>
  36. 36. Salient features: <ul><li>The only programme of its kind (in the whole world) </li></ul><ul><li>No publicity and low profile course </li></ul><ul><li>For those who want to achieve success in life – not just a degree </li></ul><ul><li>Flexible – you may stay for a month and continue the rest of the education by distance mode. / you may attend weekend classes </li></ul><ul><li>Scholarships for those from poor economic background </li></ul><ul><li>Latest and constantly changing curriculum – keeping pace with the time </li></ul><ul><li>Placement for those who are interested </li></ul><ul><li>Admissions open throughout the year </li></ul><ul><li>Latest and most advanced technologies, books and study material </li></ul>
  37. 37. Components <ul><li>Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) </li></ul><ul><li>Meditation, spiritualisation, and self development </li></ul><ul><li>Essential softwares for business </li></ul><ul><li>Business plan, Research projects </li></ul><ul><li>Participation in conferences / seminars </li></ul><ul><li>Workshops on leadership, team building etc. </li></ul><ul><li>Written submissions of research projects/articles / papers </li></ul><ul><li>Interview of entrepreneurs, writing biographies of entrepreneurs </li></ul><ul><li>Editing of journals / newsletters </li></ul><ul><li>Consultancy / research projects </li></ul><ul><li>Assignments, communication skill workshops </li></ul><ul><li>Participation in conferences and seminars </li></ul><ul><li>Group discussions, mock interviews, self development diaryng </li></ul><ul><li>Mind Power Training & writing workshop (by Dr. T.K.Jain) </li></ul>
  38. 38. Pedagogy <ul><li>Case analysis, </li></ul><ul><li>Articles from Harvard Business Review </li></ul><ul><li>Quiz, seminars, workshops, games, </li></ul><ul><li>Visits to entrepreneurs and industrial visits </li></ul><ul><li>Presentations, Latest audio-visuals </li></ul><ul><li>Group discussions and group projects </li></ul><ul><li>Periodic self assessment </li></ul><ul><li>Mentoring and counselling </li></ul><ul><li>Study exchange programme (with institutions out of India) </li></ul><ul><li>Rural development / Social welfare projects </li></ul>
  39. 39. Branches <ul><li>AFTERSCHO☺OL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs. </li></ul>
  40. 40. Case Studies <ul><li>We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs. </li></ul>
  41. 41. Basic values at AFTERSCHO☺OL <ul><li>Share to learn more </li></ul><ul><li>Interact to develop yourself </li></ul><ul><li>Fear is your worst enemy </li></ul><ul><li>Make mistakes to learn </li></ul><ul><li>Study & discuss in a group </li></ul><ul><li>Criticism is the healthy route to mutual support and help </li></ul><ul><li>Ask fundamental questions : why, when, how & where? </li></ul><ul><li>Embrace change – and compete with yourself only </li></ul>
  42. 42. social entrepreneurship for better society