Digital Assignment 1 Statistics For Engineers - Mat2001 Module 1 & 2 Submission Date: 20-9-2021
Digital Assignment 1 Statistics For Engineers - Mat2001 Module 1 & 2 Submission Date: 20-9-2021
Digital Assignment 1 Statistics For Engineers - Mat2001 Module 1 & 2 Submission Date: 20-9-2021
Module 1 & 2
1. Calculate the mean, median and mode from the following data.
Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
No. of 4 12 40 41 27 13 9 4
Students
2. Find the missing frequency from the following frequency distribution if Mean is 38.
Marks 10 20 30 40 50 60 70
No.of 8 11 20 25 ? 10 3
Students
4. An analysis of monthly wages of workers of two factories A and B yielded the following
results:
Factories
A B
No. of workers 50 60
Average monthly wages Rs.60 Rs.48
Obtain the average monthly wages of all workers taken together.
1
X 5 6 7 8 9
F 5 10 24 15 6
X = 𝑥i 0 1 2 3 4 5 6 7
𝑝i 0 a 2a 2a 3a a2 2a2 7a2+a
(i) Find the value of ‘a’. Write its distribution function and c.d.f.
1
(ii) If 𝑃(X ≤ 𝑘) > , find the least value of 𝑘.
2
10. The probability that a person will die in the time interval (𝑡1, 𝑡2) is given by
2 𝑡
𝑃(𝑡1 ≤ 𝑡 ≤ 𝑡2 ) = ∫ 𝑎(𝑡) 𝑑𝑡. The function 𝑎(𝑡) is determined from long records and can be
𝑡1
−9 2(100 − 𝑡)2, 0 ≤ 𝑡 ≤ 100
assumed to be 𝑎(𝑡) = 3X10 𝑡
0 , 𝑜𝑡ℎ𝑒𝑟𝑤i𝑠𝑒
Determine (i) The probability that person will die between the ages 60 and 70 &
(ii) The probability that he will die between those ages, assuming that he lived up to 60.
𝑎𝑥, i𝑛 0 ≤ 𝑥 ≤ 1
𝑎, i𝑛 1 ≤ 𝑥 ≤ 2
𝑓(𝑥) =
3𝑎 − 𝑎𝑥, i𝑛 2 ≤ 𝑥 ≤ 3
0, 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
13. A gun is aimed at a certain point, say, the origin of the co-ordinate system. Due to the
random factors, the actual hit point can be any point (X, 𝑌) in a circle of radius 𝑎 with center
at the origin. If the joint density function of (X, 𝑌) can be assumed as
(i) Find the value of 𝑘 and (ii) The marginal density function of X.
14. If the joint p.d.f. of a two dimensional continuous 𝑅. 𝑉. (X, 𝑌) is given by ƒ(𝑥, 𝑦) =
3(𝑥 + 𝑦), i𝑛 𝑥 > 0, 𝑦 > 0 𝑎𝑛𝑑 𝑥 + 𝑦 ≤ 1 𝑎𝑛𝑑 = 0, elsewhere, find
𝑉𝑎𝑟(X), 𝑉𝑎𝑟(𝑌) 𝑎𝑛𝑑 𝐶𝑜𝑣(X, 𝑌).
2
15. Find the characteristic function of the distribution of a discrete𝑅. 𝑉. X, whose probability
mass function is given by 𝑃(X = 𝑟) = 𝑞𝑟𝑝; 𝑟 = 0,1,2, … … . , ∞, where 𝑝 + 𝑞 = 1. Hence
find the mean and variance of the distribution.