Reasoning, Di And Mental Aptitude 10 October
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Transcript of Reasoning, Di And Mental Aptitude 10 October
www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
THEORETICAL DISTRIBUTIONS IN BUSINESS
STATISTICS AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS
CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME –
World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship
OPEN FOR ALL FREE FOR ALL
www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
THEORETICAL DISTRIBUTIONS IN BUSINESS
STATISTICS
Dr. T.K. Jain.
AFTERSCHO☺OLCentre for social entrepreneurship
Bikaner M: 9414430763
www.afterschool.tk, www.afterschoool.tk
www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
6 COINS ARE TOSSED 512 TIMES. FIND THE EXPECTED FREQUENCIES OF HEADS.
• The basic formulae:
• NCr*P^r*q^(n-r)
N = 6, r = 0 to 6, p = ½ q = ½
6c0 *(1/2)^0*(1/2)^6
=1/64
Similarly we will find value for r=1,2,3,4,5,6.
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Solution . . ..
X F(X) Expected Frequency
(EF)=(F(X)*512)
X * E.F. X^2 * E.F.
0 1/64 8 0 0
1 6/64 48 6/64 6/64
2 15/64 120 30/64 60/64
3 20/64 160 60/64 180/64
4 15/64 120 60/64 240//64
5 6/64 48 30/64 150/64
6 1/64 8 6/64 36/64
Total 1 512 3 10.5
www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
In the previous question calculate mean and standard deviations?
• Mean = Total of X * F (X)• = 3 answer. • Variance = • = difference between Total of product of X^2
* F(X) and square of Mean• =10.50 – 3^2• =10.5 – 9 = 1.5• Standard deviation is square root of 1.5 =
1.22 answer.
www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
The possibility that an experiment will succeed is ¾, what is the
probability that when this experiment is repeated 5 times, still
there are all failures?
• N = 5, R = 0, P =3/4, Q = ¼
• NCR*P^r*q^(n-r)
• =5C0*(3/4)^0*(1/4)^5
• =1*1*1/1024
• =1/1024 answer.
www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
P(X=2) = 9P(X = 4)+90P (X = 6), what is standard deviation of X , if it
follows poisson distribution?
• Basic formulae = (e^-m *m^x)/ x!• (2.71828^-m *m^2)/2 = 9* (2.71828^-m
*m^4)/24 +90 * (2.71828^-m *m^6)/720• Multiply all by 24 & divide by 3• 4*(2.71828^-m *m^2) = 3* (2.71828^-m *m^4)
+ (2.71828^-m *m^6)• =4*(2.71828^-m *m^2) -3* (2.71828^-m *m^4) -
(2.71828^-m *m^6)=0
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Solution. .
• =4*(2.71828^-m *m^2) -3* (2.71828^-m *m^4) - (2.71828^-m *m^6)=0
• =(e^-m* m^2) (4 – 3M^2 – M^4) =0• =(e^-m* m^2) (4 -4M^2 + M^2 – M^4) =0• =(e^-m* m^2) (4(1-m^2) +m^2(1-m^2)) =0• M^2 CAN BE EITHER 1 OR -4 (which is not
possible). • THUS M = 1• STANDARD DEVIATION = 1 ANSWER.
www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
If 2% of bulbs made are defective, what is the probability that out of
150 bulbs made exactly one bulb is defective. (poisson distribution)?
• M = NP = 150 *2/100 = 3; X = 1
• = (2.71828^-3 *3^1) / 1!
• =.149362 answer.
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If 2% of bulbs made are defective, what is the probability that out of 150 bulbs more than 2 bulbs are defective (poisson distribution)?
• 1 – (0 defective + 1 defective + 2 defective) = more than 2.
• M = 3; X = 0, 1,2,
• (2.71828^-3 *3^0) / 1+(2.71828^-3 *3^1) / 1!+(2.71828^-3 *3^2) / 2
• =.049+.149+.22 =.418
• Thus 1-.418 = .582 answer.
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Find poisson distribution value, p (x< = 2 / X > = 1), Mean is 2.2?
• For values of 2 or 1• (2.71828^-2.2 *2.2^2) / 2+(2.71828^-2.2*2.2^1) / 1• =.511• Let us calculate for X = 0• (2.71828^-2.2 *2.2^0) /1• =.1108• 1- .1108 = .8892• Now divide the earlier value by this value to get
answer. • =.511/.8892 = .5746 answer.
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Why such a programme?
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• You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.
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About AFTERSCHO☺OL PGPSE – the best programme for developing great
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Workshops from AFTERSCHO☺OL
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Components • Pedagogy curriculum and approach based on IIM Ahmedabad and ISB
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