in first example of lec44,how computations are carried out in A,B,C,D columns.
i want to know how those values are computed written in brackets in these columns.
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in columns main (A, B, C, D) ki values ki power 2 li hai for example : 32.3^2 = 1043.29,,,,,,34.00^2 = 1156.00
isi terahn baqi tables main bhi hai phr bi main plus kia hova hai rows ki values ko ( un values ko nahi jin ki power li hai okay) e.g 32.3 + 33.3 + 30.8 + 29.9 = 125.7 .
bi^2 main bi ki values ki bhi 2 power li hai , e.g 125.7^2 = 15800.49 baqi bhi isi terhan krni hain sari
ab last waly column main ham ny (A, B , C, D) column ki values ko plus krna hai pr woh values jo 2 ki power sy ai hain ..e.g: 1043.29+1108.89+948.64+858.49 = 3959.31..and so on...
T.j main ham my colum wise plus kr ky likhni hain (A, B, C, D) ki values ko ( jo 2 ki power sy ai hain ) eg. (column A) 32.3+34+34.3+35.0+36.5 = 172.1 and so on ...
T.j^2 main T.j ki vaues ki power leni hai 2 sy jesy bi^2 main kia tha
ab last wali row main ham ny phr sy column wise calcultions krni hain (A, B, C,D) ky column ki power wali values ko plus krna hai for. example: (column A) 1043.29+1156+1176.49+1225.00+1332.25 = 5933.03 and so on
hope you got it ..good luck
T distribution
3 question was from probability
husband and wife apply for same job and husband probability for job is like this 9/3 and wife job probability was something 3/5 like , what is the probability that husband could get job and wife not?
another question was , a boy sell umbrellas on rainy days and earn 30$ and in other days he can earn 24$ , if the probability of rain is 0.3% what will he expectation ?
another question was ,
central thuerium ,
and what is difference between constant and random variable ....
portion probability
Total marks 75
30 multiple choic
4 question of 2 marks
4 question of 3 marks
5 question of 5 marks
Sentific calculator not allowed
Multiple choice 10% from past papers
Q1.decribe about singnefince level
Q2 .discuss about center limit theorem
Q3.q about random degree
Q4.2 – 3 q about hypothesis
Some Qs are related to tdistribution .0
Q5 About Destiy function.
Total Marks 75
43 MCQ's and all MCQ's were from past papers of 2009 to 2011
Q:Not more than 70% people pay tax, formulate null and alternative hypothesis? 2 Marks
Q:Define an UnBiased estimator? 2 Marks
Q:Briefly Explain an experiment design? 2 Marks
Q:Define an independent and dependent variable in regression? 2 Marks
Q:For the data set, we find out five number summary result: Xo=200, Xm=500 and Q2=350, (3 Marks)
Q:Discuss three properties of normal distribution? 3 Marks
Q:The 90% confidence interval for the population mean is 11 to 20, interpret this result? 3 Marks
Q:Define LSD test? 3 Marks
some long questions and they are all with numerical values
Q:Correlation of Coefficient? 5 Marks
Q:Hypothesis Test? 5 Marks
Q:Confidence Interval? 5 Marks
Q:Mean and Variance of Sampling? 5 Marks
Q:Calculate Harmonic Mean of given data? 5 Marks
total question = 43 ...30 mcqs mostly from past papers rest were subjective
What is the difference between an outcome and an event? (2)
The mean of a Poisson distribution is 5 while its standard deviation is 4. Comment on it (2)
If an automobile is driven on the average no more than 16000 Km per year then formulate the null and alternative hypothesis (2)
If the population proportions are gives as: P1 = 0.4, P2 = 0.20
find sigma^2 Phat 1  Phat 2 , where n = 12.
How many parameters are associated with F distribution and what is the range of the distribution? (3)
Which of the following statement represents continuous data and discrete data? (5)
i) Number of shopes in a plaza.
ii) Hourly temperature recorded by whether bureau.
iii) Inches of rainfall in a city.
iv) Number of passengers carried by rail every year.
v) Height measurements of boys studying in a college.
The probability density function of a random variable X is given by :
f(x) 3x^2 ( 0 < or equal to x is < or equal to 1)
0 else where
calculate P(X < 0.5) (5)
Nine individual are chosen at random from a normal population and their weights in Kg are found to be 63, 64, 66, 67, 67, 68, 69, 69, 70 with mean weight 67 and standard deviation 2.345. Test the hypotheses c
Ho : mew = 66Kg. Using 5% level of significance. (5)
Two samples are drawn from two normal populations with the following information:
Lahore : n1 = 50, Xbar 1 = 14, s1 = 5
Karachi: n2 = 70, Xbar 2 = 12, s2 = 4
Construct the 95% confidence interval for the difference between the two population means. ( 5)
mean was also given
96% CI find out krna tha
we use Zstatistics
1. A sample of siz n=3 drawn without replacement expirenment from a population N=5 items whose values ,0,2,3,6,7 draw possible samples
2. Calculate sampling error if sample is 102 and population mean is 100
3. A random sample of 12 observations is drawn then a normal distribution with =33.suppose that the sample means is found to be Find 96% confidence interval for
4. RCBD with MSE=200Measure of treatments=4 no of block=5 Then find value of LSD test for
5. Define Unbiased estimator
6. Quartile deviation
7. 5 number summery
Mcqs=20 marks too much easy and 4rom old papers
subjective questions
1.what s b!as?(2)
2.advantages and disadvantages of medan?(3)
3. Mathematical expecton of discrete random variable?(3)
4.any two properties of mathematical expectation?(2)
5.what s stat!c test?(2)
6. Decide a small sample and large sample?(2)
7.4 questions were numeric 4rom probablty and bnomal dstrbuton?(2 or 3 marks)
8. Calculate the class boundaries,class marks and relatve frequency?(5)
9.2 questions k smagh na aye pata nah kasy kernay thay (5)
10.tell the null and alternative hypothesis of 150?(2)
1. A sample of siz n=3 drawn without replacement expirenment from a population N=5 items whose values ,0,2,3,6,7 draw possible samples
2. Calculate sampling error if sample is 102 and population mean is 100
3. A random sample of 12 observations is drawn then a normal distribution with =33.suppose that the sample means is found to be Find 96% confidence interval for
4. RCBD with MSE=200Measure of treatments=4 no of block=5 Then find value of LSD test for
5. Define Unbiased estimator
6. Quartile deviation
7. 5 number summery
Total 36 questions
20 mcqs
6 questions of 2 marks
6 questions of 3 marks
4 questions of 5 marks
all mcqs from previous paperz
2 marks:
level of significance
type of design
5 marks:
all questions were from test hypothesi
Total marks 75, 34 short questions. Total questions 43.
35. In which condition, Poisson distribution is used to approximate the hypergeometric distribution?
36. Elaborate the Least Significant Difference (LSD) test.
37. Write down the formula of combined or pooled proportion of two samples.
38. If approximate value of class interval is 2.96 and range = 14.8 then find the number of classes.
39. The probability density function of random variable X is given by
Find P(X < 1.5).
40. Find the coefficient of variation (C.V) for the following price of a commodity.
Price (X): 8, 13, 18, 23, 30
41. Flaws in plywood occur at random with an average of one flaw per 50 square feet. What is the probability that a 32 square feet will have no flaws?
42. Can you reject a claim that the average age of members of Parliament is at least 50, if a random sample of 36 members has a mean age of 48.7 with standard deviation of 3.1 years? Assume all members ages are normally distributed; where ().
43.
If we have and
Then, find the 90% confidence interval for population variance ( ).
Solutions of the Following Questions Required Urgently
4. find value of A in joint probabilty of f(x,y) for exp AYx/2 whereas 0<y<1, 0<x<1.
1.A random variable X is normally distributed with. Find the probability of x larger than 54.
2.A random sample of 50 observations is drawn from a normal distribution with. Suppose that the sample mean is found to be Find 95% confidence interval for
3.Find the value of chisquare from the following table.
Number of Customer Arrivals 
Observed Frequency o_{i} 
Expected Frequency e_{i} 

0 
84 
54.12 

1 
114 
108.28 

2 
70 
108.28 

3 
60 
72.16 

4 
32 
36.08 

5 
16 
14.44 

6 
15 
4.80 

7 
4 
1.36 

8 
5 
0.36 

9 or more 
0 
0.08 

4.Construct a stemandleaf display from the following data.
48, 31, 54, 37, 18, 64, 61, 43,
40, 71, 51, 12, 52, 65, 53, 42,
39, 62, 74, 48, 29, 67, 30, 49,
68, 35, 57, 26, 27, 58.
5.The p. d. f. of a r.v. is given
Calculate P(X<0.5)
6.If population proportions are given as:
Find ,where n = 10
7.Formulate the null and alternative hypothesis in each of the following.
(1) Average domestic consumption of electricity is 50 units per month.
(2) Not more than 30% people pay Zakat (tax).
10.An exercise physiologist wants to demonstrate that the average person walks more than 800 km per year. State the null and alternative hypothesis.
husband and wife apply for same job and husband probability for job is like this 9/3 and wife job probability was something 3/5 like , what is the probability that husband could get job and wife not?
a boy sell umbrellas on rainy days and earn 30$ and in other days he can earn 24$ , if the probability of rain is 0.3% what will he expectation ?
Q:The 90% confidence interval for the population mean is 11 to 20, interpret this result? 3 MarksQ:Define LSD test? 3 Marks
If an automobile is driven on the average no more than 16000 Km per year then formulate the null and alternative hypothesis (2)
If the population proportions are gives as: P1 = 0.4, P2 = 0.20
find sigma^2 Phat 1  Phat 2 , where n = 12.
The probability density function of a random variable X is given by :
f(x) 3x^2 ( 0 < or equal to x is < or equal to 1)
0 else where
calculate P(X < 0.5) (5)
Nine individual are chosen at random from a normal population and their weights in Kg are found to be 63, 64, 66, 67, 67, 68, 69, 69, 70 with mean weight 67 and standard deviation 2.345. Test the hypotheses c
Ho : mew = 66Kg. Using 5% level of significance. (5)
Two samples are drawn from two normal populations with the following information:
Lahore : n1 = 50, Xbar 1 = 14, s1 = 5
Karachi: n2 = 70, Xbar 2 = 12, s2 = 4
Construct the 95% confidence interval for the difference between the two population means. ( 5)
find the critical value of chisquare
a boy sell ambrellas on rainy days and earn 30$ and in other days he can earn 24$ , if the propability of rain is 0.3% what will he expectation ?
some data was given,find P(X>25)
1. A sample of siz n=3 drawn without replacement expirenment from a population N=5 items whose values ,0,2,3,6,7 draw possible samples
2. Calculate sampling error if sample is 102 and population mean is 100
3. A random sample of 12 observations is drawn then a normal distribution with =33.suppose that the sample means is found to be Find 96% confidence interval for
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