Questions without answers in Probability and Statistics

Which of the following statements is/are true?$Y=1+1.8 X$ and $X=1-0.5 Y$ are estimated as lines of regression of $Y$ on $X$ and $X$ on $Y$, respectively.$Y=1+1.3 X$ and ...

Let $X$ be a random variable having probability density function (pdf)$$f_X(x) =\left\{\begin{array}{ll}\dfrac{e}{2(e-1)} e^{-x}, & 0 < x < 1, \\\dfrac{1}{2}, & 1 < x < 2...

​​Let $X$ and $Y$ be two random variables with mean $0$, variance $1$, and correlation coefficient $\frac{1}{3}$. Then the value of $\operatorname{Var}(X+3 Y)$ is equal t...

There are four cities, namely, $C_{1}, C_{2}, C_{3}$ and $C_{4}$. The cities are directly connected by four roads as shown in the picture given below, that is, $C_{1}$ is...

The probability of a person telling the truth is $\frac{4}{6}$. An unbiased die is thrown by the same person twice and the person reports that the numbers appeared in bot...

In a cosmopolitan city, the population comprises of $30 \%$ female and $70 \%$ male. Suppose that $5 \%$ of female and $30 \%$ of male in the population are foreigners. A...

A survey of $450$ students about their subjects of interest resulted in the following outcome.- $150$ students are interested in Mathematics.- $200$ students are interest...