Questions without answers in Probability and Statistics

A box contains $26$ cards with all English alphabets from $\text{A}$ to $\text{Z}$.The probability of randomly choosing the card with either '$\text{E}$' or '$\text{S}$' ...

Which ONE of the following options is the CORRECT formula for Chi-Square $\left(\chi^{2}\right)$ test?Given, $O_{1}, O_{2}, \ldots . O_{n}$ are the observed values, $E_{1...

A $6$-hour rainfall of $6$ cm at a station was found to have a return period of $40$ years.The probability that a $6$ -hour rainfall of this or larger magnitude will occu...

Standard deviation for the particulate matter (PM) concentrations listed in the table is $\_\_\_\_$ $\mu \mathrm{g} / \mathrm{m}^{3}$ (rounded off to one decimal place).$...

​​​​​​Consider the following statementsEnvironmental pollutant concentration is generally modeled using lognormal distribution.Environmental pollutant concentration is ge...

A residential family is considering two cities for relocation. The data related to pollutant exposure and associated health cost per year are given in the following figur...

The probability of a boy or a girl being born is $1 / 2$. For a family having only three children, what is the probability of having two girls and one boy?$3 / 8$$1 / 8$$...

Ten cards in a pack are numbered as $1,2,3, \ldots 10$. The probability of drawing a card with an even number or a number which is a multiple of 5 from the pack is$4 / 10...

A population $\text{(with mean $\mu$)}$ follows normal distribution. Ten samples $(N)$ are drawn at random with a mean value of " $x$ " and standard deviation of " $S$ "....

Given a fair six-faced dice where the faces are labelled $'1'$, $'2'$, $'3'$, $'4'$, $'5'$, and $'6'$, what is the probability of getting a $'1'$ on the first roll of the...

A researcher compiled the following information about the performance of a kit in an outbreakInfection stateKit responseDisease (probability =0.002)Positive response (pro...

$\text{W1, W2, W3...W9}$ represent the holding times of $9$ water samples, which follow a normal distribution with mean $=8.33$ and standard deviation $=4.472$.$\text{M}$...

A biased die has six faces numbered as $k=1,2,3,4,5$, and $6$. On rolling the die, the probability of the number k appearing is proportional to $k^{2}$. What is the proba...

A student reported following arsenic concentrations in water samples:$$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \text{Arsenic concentration (mg/L)} & 0.10 & 0.12 & 0.20 & 0...

$\mathrm{X}$ is normally distributed with following data $(25.8,36.6,26.3,21.8,27.2)$. Select the correct statement about $X\left(\mathrm{t}_{\text {crit }, \alpha}=0.05,...

Ten litres of the sample was filtered through a membrane filter and the filter was transferred to solid agar media which supports growth of coliform organisms. After incu...

An individual has four different email accounts. $60 \%$ of emails come into his corporate account, $30 \%$ come into his gmail account and remaining $10 \%$ are equally ...