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Roll No.
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Total No. of Questions : 18
Total No. of Pages : 04
B.Tech. (CSE/IT) (2018 Batch) (Sem.-2)
MATHEMATICS-II
Subject Code : BTAM-204-18
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M.Code: 76257
Time: 3 Hrs.
Max. Marks : 60
- INSTRUCTIONS TO CANDIDATES :
- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- SECTION - B & C have FOUR questions each.
- Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
- Select atleast TWO questions from SECTION - B & C.
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SECTION-A
Answer the following :
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- For two events A and B such that P(A) = ½, P(B) = 1/3 and P(AUB) = ½. Find P(B/A).
- If A, B and C are three mutually exclusive and exhaustive events associated with random experiments. Find P(A) given that P(B) ==P
- If a random variable X assumes the values 0 and 1 with P (X = 0) = 3 P(X=1), then find the variance of X.
- The mean of the binomial distribution is 20 and standard deviation is 4. Calculate the parameter of its distribution.
- State Binomial and Poisson distribution.
- What is Spearman's rank correlation coefficient?
- In Poisson frequency distribution, frequency corresponding to 3 successes is 2/3 times frequency corresponding to 4 successes. Find the variance of the distribution.
- Let X be the random variable such that P (X = -2) = P (X = -1),1 P (X = 2) = P (X = 1) and P(X > 0) = P(X < 0) = P (X = 0). Obtain the probability mass function of x.
- State chi-square and Student's t-distributions.
- A computer program has produced the following output for a hypothesis-testing problem: Difference in sample means: 2.35 ; Degree of freedom : 18; Test statistics: 2.01. Find the standard error of the difference in sample means?
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SECTION-B
- a) Find the Karl Pearson's co-efficient of skewness from the following data :
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Size : 1 2 3 4 5 6 7
Frequency: 10 18 30 25 12 3 2
b) From the following table, calculate the coefficient of correlation by karl Pearson's method.
X 6 2 10 4 8
Y 9 11 ? 8 7--- Content provided by FirstRanker.com ---
Arithmetic means of X and Y series are 6 and 8 respectively. - a) Suppose that the time in minutes that a person has to wait at a certain station for a train is found to be a random phenomenon with a probability function specified by the distribution function :
0; x=0
X/2 ; 0=x<1
F(x)=<--- Content provided by FirstRanker.com ---
1/2 ; 1< x <2
X/4 ; 2=x<4
1; x=4
What is the conditional probability
?) More than 3 minutes, given that it is more than 1 minutes.--- Content provided by FirstRanker.com ---
ii) Less than 3 minutes, given that it is more than 1 minutes.
b) Two fair dice are thrown independently. Three events A, B and C is defined as follows:
A: Even face with first dice
B: Even face with second dice
C: Sum of the points on the two dice is odd.--- Content provided by FirstRanker.com ---
Discuss the independence of events A, B and C. - a) Marks obtained by a number of students are assumed to be normally distributed with mean 50 and variance 36. If four students are taken at random, what is the probability that exactly two of them will have marks over 62? Given that ?f(z)dz=0.4772 where Z is N (0, 1).
b) If 2 percent of the books bound at a certain bindery have defective bindings. Determine the probability that five of 400 books bound by this bindery will have defective bindings. - a) Service calls come to a maintenance center, according to a Poisson process and, on the average, 2.7 calls come per minute. Find the probability that (i) no more than 4 calls come in any minute, (ii) fewer than 2 calls came in any minute; (iii) more than 10 calls come in a 5-minute period.
b) If the two lines of regression are 4x – 5y + 30 = 0 & 20x – 9y – 107 = 0. Which of these is the line of regression of x on y, and y on x. Find correlation coefficients and variance of Y when variance of X is 3.
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SECTION-C
- A continuous random variable X follows the probability law f (x) = Ax², 0 = x = 1. Determine A and find the probability that (i) X lies between 0.2 and 0.5 (ii) X is less than 0.3 (iii) 1/4
3/4 given that X > 1/4 - a) The length of time a person speaks over phone follows an exponential distribution with mean 6. What is the probability that the person will talk for (i) more than 8 minutes and (ii) between 4 and 8 minutes
b) A continuous random variable X has a probability density function f (x) = k (1 + x), 2 = x = 5. Find P(X = 4) - a) Fit a second degree parabola to the following data :
X: 1 2 3 4 5
Y: 1090 1220 1390 1625 1915--- Content provided by FirstRanker.com ---
b) A reading test is given to an elementary school class that consists of 12 Anglo-American children and 10 Mexico-American children. The results of test are :
Anglo American Mexico American
Mean 74 70
Std. 8 10
Is the difference between means of the two groups significantly at the 0.05 level of significance? Value of t at 5% level for 20 degree is freedom is 2.086. - a) Before an increase in excise duty on tea, 400 people out of a sample of 500 persons were found to be tea drinkers. After an increase in duty, 400 people were tea drinkers in a sample of 600 people. Using standard error of proportion, state whether there is significant decrease in the consumption of tea at 5% level of significance. Take value of Z at 5% level of significance is 1.645.
b) The following table gives for a sample of married women, the level of education and marriage adjustment score :
Marriage adjustment score
Very low Low High Very High
College 24 97 62 58--- Content provided by FirstRanker.com ---
Level of High School 22 28 30 41
Education Middle school 32 10 11 20
Can you conclude from the above, the higher the level of education, the greater is the degree of adjustment in marriage? Use table value of chi-square at 5% level for 6d.f. = 12.59.
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This download link is referred from the post: PTU B.Tech 1st Semester Last 10 Years 2009-2019 Previous Question Papers|| Punjab Technical University
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