JNTU B.Tech I Year MATHEMATICS-III Previous Question Paper (March/April - 2023 - R16)

Define Probability Mass function and Probability Density function.

If X is a continuous random variable with probability function f(X=x) = k e^-2x, x>0, then find k.

Define Point Estimation and Interval Estimation.

Write the assumptions of t- test?

Define Null Hypothesis and Alternative Hypothesis.

Define type I and type II error.

Explain the iteration method to solve an equation.

Write a normal equations to fit a second degree curve of the form y = a + bx + cx² for the given data.

Using Euler’s method to find y(0.2), given that dy/dx = x² + y², y(0) = 1.

Derive a formula to find the cube root of N using Newton-Raphson method.

The probability distribution function of X is given for X values {0, 1, 2, 3, 4, 5, 6} with probabilities {K, 3k, 5k, K, K, 11k, 13k}. (i) Find k (ii) Find P(X < 4), P(X ≥ 5), P(3 < X ≤ 6).

Derive moment generating function of Binomial distributions hence find mean and variance.

X is a normal variate with mean 30 and S.D 5, find the probabilities for (i) 26 ≤ X ≤ 40 (ii) X ≥ 45 (iii) |X - 30| > 5.

A manufacturer of cotter pins knows that 5% of his product is defective. Pins are sold in boxes of 100. He guarantees that not more than 10 pins will be defective. Determine the probability that a box will fail to meet the guarantee.

i) Find the value of P(0.025 < T < 0.05). ii) Find ‘k’ such that P(k < T < -1.761) = 0.045.

Explain the test procedure for equality of two means in small sample tests.

Two treatments have applied on 500 agricultural plots. Test whether treatments are independent with data: Treatment-I (208, 92), Treatment-II (32, 168).

A random sample of size 81 was taken whose variance is 20.25 and mean is 32, construct 98% confidence interval.

To test the significance of variation in the retail prices of a commodity in Mumbai (16, 8, 12, 14), Kolkata (14, 10, 10, 6) and Delhi (4, 10, 8, 8). Do the data indicate that the price in the three cities are significantly different?

In a sample of 1000 people in Maharashtra 540 are rice eaters and the rest are wheat eaters. Can we assume that both rice and wheat are equally popular in Maharashtra at 1% level of Significance?

Write a test procedure to test the equality of two proportions?

Describe about ANOVA one way classification.

By using bisection method, find an approximate root of the equation sin x = 1/x that lies between x=1 and x=1.5.

Solve by Gauss-Seidel method: 20x + y - z = 17, 3x + 20y - z = -18, 2x - 3y + 20z = 25.

Fit a second degree parabola to: X={1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0}, Y={1.1, 1.3, 1.6, 2.0, 2.7, 3.4, 4.1}.

An experiment gave values for v and t as follows: v={350, 400, 500, 600}, t={61, 26, 7, 26}. Given v = a * t^b, find the best possible values of a and b.

Evaluate the integral of 1/(1+x) dx from 0 to 1 by using: i) Trapezoidal rule (h=1/4), ii) Simpson’s 1/3 rule (h=1/4), iii) Simpson’s 3/8 rule (h=1/6).

Given dy/dx = 1 + xy and y(0) = 1, Compute y(0.1) and y(0.2) using Picard’s Method.