Recent questions and answers in Probability and Statistics / GO Instrumentation

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GATE IN 2021 | Question: 37
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 $Y\sim U\left ( 1,4 \right )$. Then $P\left ( Y\leq X \right )$ is equal to __________________ (rounded off to two decimal places).

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

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GATE2020 IN: 32
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 $3$ Red and $7$ Green balls. A bag is picked at random and a ball is drawn from it, which was found to be Red. The probability that the Red ball came from bag $B1$ $\text{(rounded off to one decimal place)}$ is ______.

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...

soujanyareddy13

2.7k points

soujanyareddy13 asked Nov 3, 2020

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3

GATE2020: 16
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 ball twice. Considering each attempt to be independent, the probability that this player puts the ball into the basket only in the second attempt $\text{(rounded off to two decimal places)}$ is __________

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...

soujanyareddy13

2.7k points

soujanyareddy13 asked Nov 3, 2020

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4

GATE2019 IN: 3
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 second ball drawn is green is 4/15 7/16 ½ 8/15

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...

Arjun

2.9k points

Arjun asked Feb 10, 2019

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5

GATE2019 IN: 27
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 probability density function, the value of A should be equal to $\mu$ – 1 $\mu$ + 1 1/($\mu$ – 1) 1/($\mu$ +1)

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 ...

Arjun

2.9k points

Arjun asked Feb 10, 2019

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6

GATE2016-27
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 color. The probability of getting a red ball in the next draw is $\frac{65}{156}$ $\frac{67}{156}$ $\frac{79}{156}$ $\frac{89}{156}$

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...

Milicevic3306

7.9k points

Milicevic3306 asked Mar 26, 2018

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7

GATE2015-36
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, $3$ are defective is 0.001 0.057 0.107 0.3

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...

Milicevic3306

7.9k points

Milicevic3306 asked Mar 26, 2018

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8

GATE2015-37
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 $g_X(x)=e^{3x/4}$ is __________ .

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}...

Milicevic3306

7.9k points

Milicevic3306 asked Mar 26, 2018

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9

GATE2014-2
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 __________.

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 __________....

Milicevic3306

7.9k points

Milicevic3306 asked Mar 25, 2018

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10

GATE2013-16
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 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$

Milicevic3306

7.9k points

Milicevic3306 asked Mar 25, 2018

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11

GATE2012-26
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$

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$

Milicevic3306

7.9k points

Milicevic3306 asked Mar 25, 2018

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12

GATE2012-3
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 $1/2$ is $3/4$ $9/16$ $1/4$ $2/3$

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 $1/2$...

Milicevic3306

7.9k points

Milicevic3306 asked Mar 25, 2018

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13

GATE2018IN: 27
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 and B are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red? 20% 25% 30% 40%

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...

gatecse

1.4k points

gatecse asked Feb 20, 2018

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14

GATE2018IN: 5
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 $\frac{5}{16}$ $\frac{3}{16}$ $\frac{3}{5}$ $\frac{9}{16}$

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...

gatecse

1.4k points

gatecse asked Feb 20, 2018

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15

GATE2018IN: 3
X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X – Y. The variance of Z is 0 1 2 3

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

gatecse

1.4k points

gatecse asked Feb 20, 2018