List of top Statistical Science Questions

The value of the integral \(I = \int_{0}^{1} \frac{1}{1+x} dx\) by using Simpson's one-third rule with \(h = 0.5\) is

The line \(y = L\) is a horizontal asymptote of the graph of the function \(f\) if

Find the interval in which the graph of the function given by \(f(x) = x^4 - 4x^3 + 10\) is concave up.

The value of \(\int_{0}^{\infty} x^7 e^{-x^2} dx\) is

The point at which the tangent to the curve \(y = x^3 - 3x^2 - 9x + 7\) is parallel to the x-axis is

Find constants a and b so that \(\lim_{x \to 0} \left( \frac{a}{2x} + \frac{a}{2} + b \right) = 1\)

Find the value of \(\int_{-1}^{2} |x| \, dx\)

A bowl contains eight chips. Three of the chips are red and the remaining five are blue. Two chips are to be drawn successively, at random and without replacement. What is the probability that the first draw results in a red chip and that the second draw results in a blue chip?

A random variable \(X\) has the following pdf:
\[ f(x) = \frac{1}{\sqrt{12\pi}} e^{-\frac{(x-1)^2}{6}}; \quad -\infty < x < \infty \]
\(= 0\), otherwise.
Then \(\int_{1}^{\infty} f(x)dx = ?\)

Which is the following statement is true?

The annual precipitation data of a city is normally distributed with mean \(1200\text{mm}\) and standard deviation \(200\text{mm}\), respectively. The probability that annual precipitation will be more than \(1400\text{mm}\)

A die is thrown 100 times. Getting an even number is considered a success. The variance of the number of successes is:

In a binomial distribution the mean is 8 and variance is 6. Then the mode is:

The coefficient of variation of Poisson distribution with mean 36 is:

The probability of occurrence of two events \(A\) and \(B\) are 0.25 and 0.50 respectively. The probability of their simultaneous occurrence is 0.14. The probability that neither \(A\) occurs nor \(B\) occurs is:

Which one of the following is a correct statement?

A scooter rider covers a certain distance at a uniform speed of \(45\text{ km}\) per hour and retraces the same path at a uniform speed of \(55\text{ km}\) per hour to reach the starting point. His average speed during the whole journey is:

The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class is 10.6. Which one of the following is the upper class boundary of the highest class?

The median of a given frequency distribution is found graphically with the help of:

A frequency distribution can be presented graphically by:

If \(X \sim N(\mu, \sigma^2)\). The maximum ordinate is at \(X = \mu\) and is given by:

The unit of coefficient of correlation is:

The mean weight per bag in a group of 6 bags of rice is \(119\text{ kg}\). The individual weights of 5 of them are \(115\text{ kg}\), \(109\text{ kg}\), \(129\text{ kg}\), \(117\text{ kg}\) and \(114\text{ kg}\). What is weight of the other bag of the group?

If \(X\) is a random Poisson variate with \(P(X=1) = P(X=2)\). Then \(P(X=4)\) is:

The arithmetic mean of n number series is $\bar{x}$. The sum of last n-1 numbers is k. Then the first number will be: