JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year COMPUTATIONAL STATISTICS Previous Question Paper (March - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
Solve
Answer
To solve the linear congruence 7x ≡ 4 (mod 11), we need to find the modular multiplicative inverse of 7 modulo 11. We look for an integer y such that 7y ≡ 1 (mod 11).
Testing values for y:
- 7(1) = 7 ≡ 7 (mod 11)
- 7(2) = 14 ≡ 3 (mod 11)
- 7(3) = 21 ≡ 10 (mod 11)
- 7(8) = 56 = 5(11) + 1 ≡ 1 (mod 11)
The modular inverse of 7 modulo 11 is 8. Multiplying both sides of the original congruence by 8:
Since 56 ≡ 1 (mod 11) and 32 ≡ 10 (mod 11), we get:
Find x if possible such that
Answer
We have the system of congruences:
From the first congruence, we can write x = 7k + 2 for some integer k. Substituting this into the second congruence:
To solve for k, we find the inverse of 7 modulo 10. By inspection, 7 × 3 = 21 ≡ 1 (mod 10). Multiplying both sides by 3:
Thus, k = 10m + 3 for some integer m. Substituting this back into the expression for x:
Therefore, the solution is x ≡ 23 (mod 70).
For the continuous probability function
Answer
Sign in to view the complete answer paper.
Two dice are thrown 5 times. If getting a doublet is a success. Find the probability that getting the success i) At least once. ii) Two times.
Answer
Sign in to view the complete answer paper.
200 digits were chosen at random from a set of tables. The frequencies of the digits were:
| Digits | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Frequency | 18 | 19 | 23 | 21 | 16 | 25 | 22 | 20 | 21 | 15 |
Use
Answer
Sign in to view the complete answer paper.
The standard deviation of heights of students is 10 cms. A sample of 196 students was taken and the mean is 170 cms. Is this sample has been taken from a large population whose mean is 175 cms.
Answer
Sign in to view the complete answer paper.
A simple sample of heights of 6400 Englishmen has a mean of 67.85 and Standard deviation of 2.56 inches. While a simple sample of heights of 1600 Australian has a mean of 68.55 and a S.D. of 2.52 inches Test the significance between the two mean.
Answer
Sign in to view the complete answer paper.
There are three stores of groceries. There will be a shift from one store to another. A study was made on January first and it was found that 1/4 was shopped at store 1, 1/3 at 2 and 5/12 at 3. Every month store 1 retain 90% of their customers and 10% transformed to store 2. Store 2 retain 5% of their customers and 85% transformed to store and 10% to store 3. Store 3 retain 40% of their customers and 50% transformed to store 1 and 10% to store 2.
a) What proportion of customers retain by Feb 1st and March 1st
b) Find the long run proportions.
Answer
Sign in to view the complete answer paper.
Solve
Answer
Sign in to view the complete answer paper.
Solve
Answer
Sign in to view the complete answer paper.
Calculate the coefficient of correlation and the two lines of regression between the two variables x and y.
| x | 14 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
|---|---|---|---|---|---|---|---|---|---|
| y | 84 | 78 | 70 | 75 | 66 | 67 | 62 | 58 | 60 |
Answer
Sign in to view the complete answer paper.
Find whether the following is a regular transition matrix
Answer
Sign in to view the complete answer paper.
Find the equilibrium vector of
Answer
Sign in to view the complete answer paper.