List of top Statistics Questions

Find the limit of \( \left(1 + \frac{1}{n}\right)^n \) as \(n \to \infty\).
In a negatively skewed distribution, what is the correct relationship between the Mean, Median, and Mode?
What is the value of the integral \( \displaystyle \int_{-\infty}^{\infty} e^{-x^2}\,dx \)?
Which test is most appropriate for testing the significance of the difference between two small sample means?
A bag contains \(5\) red and \(7\) blue balls. If two balls are drawn at random, what is the probability that both are red?
If the correlation coefficient between \(X\) and \(Y\) is \(0.8\), what is the coefficient of determination?
In Simple Random Sampling Without Replacement (SRSWOR), what is the probability of selecting a specific unit at the second draw?
What is the rank of a \(3 \times 3\) identity matrix added to a \(3 \times 3\) null matrix?
In a Normal distribution, what percentage of data falls within two standard deviations of the mean?
If a matrix \(A\) has eigenvalues \(2\) and \(3\), what are the eigenvalues of the matrix \(A^2\)?
Which property of an estimator is satisfied if its expected value equals the population parameter?
For a Poisson distribution where the mean is \(4\), what is the value of the third central moment?
Write the important assumptions of ANOVA.
Equations of two lines of regression are \( 2x - 5y + 33 = 0 \) and \( 3x - 9y - 108 = 0 \). Which one is the regression line of \( y \) on \( x \)?
In bivariate data following results were obtained.
Mean value of X = 53, Mean value of Y = 27, byx = -1.5, bxy = 0.2. Find the regression equation of X on Y and Y on X.
A random sample from a population is given below. 35, 45, 40, 42, 39, 55 and 63. Obtain the moment estimator of the population mean.
A random sample of 100 is taken from a population. The mean and standard deviation are respectively 76 and 12. Obtain a 99% confidence interval for the mean of the population.
Find the derivative of \( y = x^6 + 48x^3 + 24x - 16 \) with respect to \( x \).
Regression analysis is a mathematical measure of the _______ of relationship between two or more variables.
The time taken by a student to reach the school is an example of _______ variable.
Which among the following is an example of +ve correlation?
X+2Y=5 and 2X+3Y=8. Find the Mean of X and Y.
A good estimator should be _______.
The ratio of two independent chi-square variables is _______.
If \( b_{xy} = - 0.3 \) and \( b_{yx} = - 0.6 \), then the value of correlation coefficient is ------------.