List of top Statistics Questions on Random variables

The time taken by a student to reach the school is an example of _______ variable.

The ratio of two independent chi-square variables is _______.

The number of petals in a flower is an example of ----------- random variable.

E(X) = 4 then E(X - 2) = ------------

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

Let \( X_1, X_2, X_3 \) be three uncorrelated random variables with common variance \( \sigma^2<\infty \). Let \( Y_1 = 2X_1 + X_2 + X_3 \), \( Y_2 = X_1 + 2X_2 + X_3 \), and \( Y_3 = X_1 + X_2 + 2X_3 \). Then which of the following statements is/are true?

For \( \alpha>0 \), let \[ \{ X^{(\alpha)}_n \}_{n \geq 1} \text{ be a sequence of independent random variables such that} \quad P(X^{(\alpha)}_n = 1) = \frac{1}{n^{2\alpha}} = 1 - P(X^{(\alpha)}_n = 0). \] Let \( S = \{ \alpha>0 : X^{(\alpha)}_n \text{ converges to } 0 \text{ almost surely as } n \to \infty \}. \) \text{Then the infimum of \( S \) equals} _________ \text{ (round off to 2 decimal places).}

Let \( X \) be a non-constant positive random variable such that \( E(X) = 9 \). Then which one of the following statements is true?