List of top Statistics Questions

A cold drinks bottling plant produces 1% defective bottles. The probability that there will be no defective in a lot of 100 bottles is nearest to:

For a uniform distribution in the range \([0, k]\), the mean and the variance are equal if:

Three functions \(F_1(x)\), \(F_2(x)\) and \(F_3(x)\) are defined below:

(i) \(F_1(x) = 0\), for all \(x \in (-\infty, +\infty)\)
(ii) \(F_2(x) = 1\), for all \(x \in (-\infty, +\infty)\)
(iii) \(F_3(x) = 0\), for all \(x \le 0\) and \(F_3(x) = 1\), for all \(x > 0\)

Which of the above functions is a distribution function of a random variable?

Three numbers \(X\), \(Y\), \(Z\) are randomly drawn from the set \(\{1, 2, 3, 4\}\). \(E(XYZ)\) is equal to:

If a random variable \(X\) has mean 3 and standard deviation 5, then the variance of \(Y = 2X - 5\) is:

If \(P(A) = 0.25\), \(P(B|A) = 0.5\), \(P(B|\bar{A}) = 0.75\) then \(P(A|B)\) is ______.

The statements below relate to Bayes theorem in probability:

(i) Bayes theorem gives a formula to compute conditional probability.
(ii) The posterior probability computed by Bayes theorem supersedes the prior probability.
(iii) Bayes theorem can be used to compute probabilities of past events on the basis of the occurrences of subsequent events.

Identify the correct answer:

A student studies for (X) number of hours during a randomly selected school day. The probability that (X) can take the values, has the following form, where (k) is some constant.
(P(X = x) = 0.2, & if x = 0
kx, & if x = 1 or 2
k(6 - x), & if x = 3 or 4
0, & otherwise )
The probability that the student studies for at most two hours is

The value of \(\lim_{x \to 1} \frac{x^3-1}{x-1}\) is

If, \(y = x^{\tan(x)}\), then \(\frac{dy}{dx}\) at \(x = \frac{\pi}{4}\), is

Let, random variable \(X \sim \text{Bernoulli}(p)\). Then, \(\beta_1\) is

Three urns contain 3 green and 2 white balls, 5 green and 6 white balls and 2 green and 4 white balls respectively. One ball is drawn at random from each of the urn. Then, the expected number of white balls drawn, is

Let \(X_1, X_2, X_3\) be three variables with means 3, 4 and 5 respectively, variances 10, 20 and 30 respectively and \(cov (X_1, X_2) = cov (X_2, X_3) = 0\) and \(cov (X_1, X_3) = 5\). If, \(Y = 2X_1 +3X_2+4X_3\) then, Var(\(Y\)) is:

Moment generating function of a random variable Y, is \( \frac{1}{3}e^t(e^t - \frac{2}{3}) \), then E(Y) is given by

If, \(f(X) = \frac{C\theta^x}{x}\); \(x = 1,2, \dots\); \(0<\theta<1\), then E(X) is equal to

If, \(f(x; \alpha, \beta) = \begin{cases} \alpha \beta x^{\beta-1} e^{-\alpha x^\beta} & ; x>0 \text{ and } \alpha, \beta>0 \\ 0 & ; \text{otherwise} \end{cases}\), then the probability density function of \(Y=x^\beta\) is

If \(f(X) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}; -\infty<x<\infty\) and \(Y = |X|\), then E(Y) is

A cyclist covers first five kilometers at an average speed of 10 k.m. per hour, another three kilometers at 8 k.m. per hour and the last two kilometers at 5 k.m. per hour. Then, the average speed of the cyclist during the whole journey, is

If, \(f(x, y) = xe^{-x(y+1)}; x \ge 0, y \ge 0\), then \(E(Y|X = x)\) is

Minimum number of replications required, when the coefficient of the variation for the plot values is given to be 12%, for an observed difference of 10% among the sample means to be significant at 5% level, is

Let, X and Y be independent and identically distributed Poisson(1) variables. If, Z = min(X, Y) then, P(Z = 1) is:

A card is drawn at random from a standard deck of 52 cards. Then, the probability of getting either an ace or a club is:

It is given that at x = 1, the function \(f(x) = x^4 - 62x^2 + ax + 9\), attains its maximum value in the interval \([0, 2]\). Then, the value of 'a' is

Consider the probability density function \( f(x;\theta) = \begin{cases} \frac{2x}{5\theta} & ; 0 \le x \le \theta \\ \frac{2(5-x)}{5(5-\theta)} & ; \theta \le x \le 5 \end{cases} \) For a sample of size 3, let the observations are, \( x_1 = 1, x_2 = 4, x_3 = 2 \). Then, the value of likelihood function at \( \theta=2 \) is

In a binomial distribution consisting of five independent trails, the probability of 1 and 2 success are 0.4096 and 0.2048 respectively. Then, the parameter 'p' of distribution is