Recent questions tagged 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...

​​​A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained:The sum of Yellow balls and twice the number ...

​​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...

The density of an amorphous polymer is $0.77 \mathrm{~g} \mathrm{~cm}^{-3}$ and that of its crystalline counterpart is $0.99 \mathrm{~g} \mathrm{~cm}^{-3}$. The density o...

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 propagation step of a free radical copolymerization is represented by the following possible reaction steps:$\text{P1}$: $M_{1}^{*}+M_{1} \rightarrow M_{1}^{*}, \quad...

In an engineering college of $10,000$ students, $1,500$ like neither their core branches nor other branches. The number of students who like their core branches is $1 / 4...

The pie charts depict the shares of various power generation technologies in the total electricity generation of a country for the years $2007$ and $2023$. The renewable ...

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...