Recent activity in Probability and Statistics

A box contains three apples and two oranges. Two fruits are removed randomly in succession. The probability that the first is an apple and the second is an orange is $\_\...

A data set is given to be $[1,2,0,-1,-3,1,2,0,1]$.The median of the data set is $\_\_\_\_$ . (rounded off to the nearest integer)

A random variable $X$ has a probability density function$$f_{X}(x)=\begin{cases} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{cases}$$The probability of $X>2$ is $...

The readings recorded from a $20$ -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04~ x+10.32$. The regression coefficient ...

Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have ...

The probability of a student missing a class is $0.1$. In a total number of $10$ classes, the probability that the student will not miss more than one class is __________...

The probability that a communication system will have high fidelity is $0.81$. The probability that the system will have both high fidelity and high selectivity is $0.18$...

A voltage $V_1$ is measured $100$ times and its average and standard deviation are $100$ V and $1.5$ V respectively. A second voltage $V_2$, which is independent of $V_1...

The figure shows the schematic of a production process with machines $A, B$ and $C$. An input job needs to be pre-processed either by $A$ or by $B$ before it is fed to $C...

Two ammeters $A_1$ and $A_2$ measure the same current and provide readings $I_1$ and $I_2,$ respectively. The ammeter errors can be characterized as independent zero mea...

A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are re...

$X$ is a discrete random variable which takes values $0,1$ and $2.$ The probabilities are $P(X=0)=0.25$ and $P(X=1)=0.5$. With $E[ .]$ denoting the expectation operator, ...

Five measurements are made using a weighing machine, and the readings are $80 \mathrm{~kg}, 79 \mathrm{~kg}, 81 \mathrm{~kg}, 79 \mathrm{~kg}$ and $81 \mathrm{~kg}$. The ...

Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\l...

Consider two identical bags $B1$ and $B2$ each containing $10$ balls of identical shapes and sizes. Bag $B1$ contains $7$ Red and $3$ Green balls, while bag $B2$ contains...

A player throws a ball at a basket kept at a distance. The probability that the ball falls into the basket in a single attempt is 0.1. The player attempts to throw the ba...

A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and...

The function p(x) is given by p(x) = A/x$^\mu$ where A and $\mu$ are constants with $\mu$ 1 and 1 $\le$ x <$\infty$ and p(x) = 0 for -$\infty$ < x <1. For p(x) to be a ...

Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green balls. Bag B has 30% red balls,60% green balls and 10% yellow balls. Contents of Bags A...

Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. The probability of getting the head for the third time in the fifth toss is$\f...

X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X – Y. The variance of Z is0123

An urn contains $5$ red and $7$ green balls. A ball is drawn at random and its color is noted. The ball is placed back into the urn along with another ball of the same co...

The probability that a thermistor randomly picked up from a production unit is defective is $0.1$. The probability that out of $10$ thermistors randomly picked up, $3$ ar...

The probability density function of a random variable $X$ is $P_X(x)=e^{-x}$ for $x\underline{>} 0$ and $0$ otherwise. The expected value of the function $g_X(x)=e^{3x/4}...

Given that $x$ is a random variable in the range $[0,\infty]$ with a probability density function $\frac{e \frac{-x}{2}}{K}$, the value of the constant $K$ is __________.

A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0<x<\propto$. Then $\text{P{X>1}}$ is $0.368$$0.5$$0.632$$1.0$

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is$1/3$$1/2$$2/3$$3/4$

Two independent random variables $\text{X}$ and $\text{Y}$ are uniformly distributed in the interval $[-1, 1]$. The probability that max$\text{[X, Y]}$ is less than $1/2$...