iare.ac.in B.Tech Probability And Statistics Semester II Question Paper : Institute Of Aeronautical Engineering

Name of the Organisation : Institute Of Aeronautical Engineering
Exam : B.Tech Semester Examinations
Subject : Probability And Statistics
Semester : 2
Document Type : Previous Question Paper
Website : https://www.iare.ac.in

B.Tech Semester II Probability And Statistics Question Papers

Institute Of Aeronautical Engineering (IARE) B.Tech Probability And Statistics Previous Question Paper Semester II for the year 2021.

Related / Similar Question Paper : iare.ac.in B.Tech Mathematical Techniques Semester II Question Paper

B.Tech Semester II Engineering Mechanics Questions

MODULE – I
1. (a) Explain the concepts:
i) Random variables and its types
ii) Probability mass and density functions [7M]
(b) Given that f(x)=k/2x is a probability distribution for a random variable that can take on the values x=0, 1, 2, 3 and 4.
i) Find k ii) Find the Cumulative probability distribution F(x) [7M]

MODULE – II
2. (a) State Binomial distribution. Determine the mean and variance of a binomial distribution. [7M]
(b) On an average a certain intersection results in 3 traffic accidents per month. obtain the probability that for any given month at this intersection.
i) Exactly 5 accidents will occur
ii) Less than 3 accidents will occur
iii) Atleast 2 accidents will occur [7M]

MODULE – III
3. (a) A researcher wished to determine if a person’s age is related to the number of hours, he or she exercises per week. The data obtained from a sample is given in Table 1. State your opinion based on Karl Pearsons’s coefficient of correlation for the data. [7M]
Table 1
Age x 18 26 32 38 52 59
Hours y 10 5 2 3 1.5 1
(b) Show that the coefficient of correlation lies between -1 and 1. [7M]

4. (a) Raw material used in the production of a synthetic fiber is stored in a place which has no humidity control. Measurements of the relative humidity in the storage place and the moisture content of a sample of the raw material (both in percentages) on five days yielded the following results shown in Table 2:
Table 2
Humidity x 42 35 50 43 48
Moisture content y 12 8 14 9 11
i) Make a scatter plot to verify that it is reasonable to assume that the regression of y on x is linear.
ii) Fit a straight line by the method of least squares. [7M]
(b) The value of Karl Pearson’s correlation (r) for the data given in Table 3 is 0.636.
Table 3
x 0.05 0.14 0.24 0.30 0.47 0.52 0.57 0.61 0.67 0.72
y 1.08 1.15 1.27 1.33 1.41 1.46 1.54 2.72 4.01 9.63
(i) Calculate the Spearman’s rank correlation for this data.
(ii) Obtain the advantage of ρ brought out in this problem? [7M]

MODULE – IV
5. (a) Explain the terms:
i) Null hypothesis ii) Alternative hypothesis iii) Critical region [7M]
(b) If a 1-gallon can of paint covers on an average 513 square feet with a standard deviation of 31.5 square feet, Calculate the probability that the mean area covered by a sample of 40 of these 1-gallon cans will be anywhere from 510 to 520 square feet? [7M]

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