GO Electrical - Recent questions and answers in Probability & Statistics
https://ee.gateoverflow.in/qa/engineering-mathematics/probability-%26-statistics
Powered by Question2AnswerAnswered: GATE2014-2-GA-6
https://ee.gateoverflow.in/542/gate2014-2-ga-6?show=1300#a1300
Kaliningrad is part of Russia after world war-2. So, it is not the contiguous region of Russia<br />
<br />
Ans will be B)Probability & Statisticshttps://ee.gateoverflow.in/542/gate2014-2-ga-6?show=1300#a1300Fri, 13 Sep 2019 14:46:11 +0000Answered: GATE2014-2-2
https://ee.gateoverflow.in/548/gate2014-2-2?show=864#a864
<table border="1" cellpadding="1" style="width:500px; border-spacing: 1px;">
<tbody>
<tr>
<td>X</td>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
</tr>
<tr>
<td>P(X)</td>
<td>k</td>
<td>2k</td>
<td>3k</td>
<td>4k</td>
<td>5k</td>
<td>6k</td>
</tr>
</tbody>
</table>
<p>where, k is a proportional constant.</p>
<p>∑P(X)=1</p>
<p>k+2k+3k+4k+5k+6k = 1</p>
<p>k= 1/21</p>
<p>P(3 dots) = 3* 1/21 =3/21 (Answer)</p>Probability & Statisticshttps://ee.gateoverflow.in/548/gate2014-2-2?show=864#a864Sat, 04 Nov 2017 01:43:55 +0000GATE2013-11
https://ee.gateoverflow.in/677/gate2013-11
<p>A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0< x< \infty$. then $P\{X> 1\}$</p>
<ol style="list-style-type:upper-alpha">
<li>$0.368$</li>
<li>$0.5$</li>
<li>$0.632$</li>
<li>$1.0$</li>
</ol>Probability & Statisticshttps://ee.gateoverflow.in/677/gate2013-11Sat, 11 Feb 2017 23:24:29 +0000GATE2014-3-4
https://ee.gateoverflow.in/615/gate2014-3-4
<p>Lifetime of an electric bulb is a random variable with density $f(x)=kx^2$ , where $x<em>$</em> is measured in years. If the minimum and maximum lifetimes of bulb are $1$ and $2$ years respectively, then the value of k is ________.</p>Probability & Statisticshttps://ee.gateoverflow.in/615/gate2014-3-4Sat, 11 Feb 2017 23:23:38 +0000GATE2014-3-GA-5
https://ee.gateoverflow.in/606/gate2014-3-ga-5
<p>The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination.</p>
<p>$\begin{array}{|c|c|c|c|c|} \hline \text{Q No} & \text{Marks} & \text{Answered Correctly} & \text{Answered Wrongly} & \text{Not Attempted} \\ \hline 1 & 2 & 21 & 17 & 6 \\ \hline 2 & 3 & 15 & 27 & 2 \\ \hline 3 & 2 & 23 & 18 & 3 \\ \hline \end{array}$</p>
<p>What is the average of the marks obtained by the class in the examination?</p>
<ol style="list-style-type:upper-alpha">
<li>$1.34$</li>
<li>$1.74$</li>
<li>$3.02$</li>
<li>$3.91$</li>
</ol>Probability & Statisticshttps://ee.gateoverflow.in/606/gate2014-3-ga-5Sat, 11 Feb 2017 23:23:16 +0000GATE2014-3-GA-9
https://ee.gateoverflow.in/610/gate2014-3-ga-9
<p>The ratio of male to female students in a college for five years is plotted in the following line graph If the number of female students in $2011$ and $2012$ is equal, what is the ratio of male students in $2012$ to male students in $2011$?</p>
<p style="text-align:center"><img alt="" height="246" src="http://ee.gateoverflow.in//?qa=blob&qa_blobid=8303112599809053281" width="407"></p>
<ol style="list-style-type:upper-alpha">
<li>$1:1$</li>
<li>$2:1$</li>
<li>$1.5:1$</li>
<li>$2.5:1$</li>
</ol>Probability & Statisticshttps://ee.gateoverflow.in/610/gate2014-3-ga-9Sat, 11 Feb 2017 23:23:16 +0000GATE2014-2-27
https://ee.gateoverflow.in/573/gate2014-2-27
Let $X$ be a random variable with probability density function<br />
<br />
$f(x)=\begin{cases} 0.2,& \text{for } \mid x \mid \leq 1\\ 0.1,& \text{for }1< \mid x \mid \leq 4\\ 0 & \text{otherwise } \end{cases} \\$<br />
<br />
The probability $P(0.5 < X < 5)$ is ______.Probability & Statisticshttps://ee.gateoverflow.in/573/gate2014-2-27Sat, 11 Feb 2017 23:22:50 +0000GATE2014-2-GA-9
https://ee.gateoverflow.in/545/gate2014-2-ga-9
<p>The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in $2009$, by what percent did the number of male students increase in $2009?$</p>
<p style="text-align:center"><img alt="" src="http://ee.gateoverflow.in//?qa=blob&qa_blobid=10008816630421437028"></p>
Probability & Statisticshttps://ee.gateoverflow.in/545/gate2014-2-ga-9Sat, 11 Feb 2017 23:22:23 +0000GATE2014-1-27
https://ee.gateoverflow.in/508/gate2014-1-27
<p>A fair coin is tossed $n$ times. The probability that the difference between the number of heads and tails is $(n-3)$ is</p>
<ol style="list-style-type:upper-alpha">
<li>$2^{-n}$</li>
<li>$0$</li>
<li>$^{n}C_{n-3}2^{-n}$</li>
<li>$2^{-n+3}$</li>
</ol>Probability & Statisticshttps://ee.gateoverflow.in/508/gate2014-1-27Sat, 11 Feb 2017 23:21:53 +0000GATE2015-2-27
https://ee.gateoverflow.in/443/gate2015-2-27
<p>Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $H$ represents head and $T$ represents tail. Which one of the following is TRUE?</p>
<ol style="list-style-type:upper-alpha">
<li>The coin tosses are independent.</li>
<li>R is fair, S is not.</li>
<li>S is fair, R is not.</li>
<li>The coin tosses are dependent.</li>
</ol>Probability & Statisticshttps://ee.gateoverflow.in/443/gate2015-2-27Sat, 11 Feb 2017 23:20:53 +0000GATE2015-1-29
https://ee.gateoverflow.in/379/gate2015-1-29
<p>Two players, $A$ and $B$, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $A$ starts the game, the probability that $A$ wins the game is</p>
<ol style="list-style-type:upper-alpha">
<li>$5/11$</li>
<li>$1/2$</li>
<li>$7/13$</li>
<li>$6/11$</li>
</ol>Probability & Statisticshttps://ee.gateoverflow.in/379/gate2015-1-29Sat, 11 Feb 2017 23:18:25 +0000GATE2015-1-1
https://ee.gateoverflow.in/351/gate2015-1-1
A random variable $X$ has probability density function $f(x)$ as given below:<br />
<br />
$ f(x)= \begin{cases} a+bx & \text{ for } 0 < x < 1 \\ 0 & \text{otherwise} \end{cases}$<br />
<br />
If the expected value $E[x] = 2/3$, then $Pr[x < 0.5]$ is __________.Probability & Statisticshttps://ee.gateoverflow.in/351/gate2015-1-1Sat, 11 Feb 2017 23:18:23 +0000GATE2015-1-GA-8
https://ee.gateoverflow.in/348/gate2015-1-ga-8
<p>The pie-chart below has the breakup of the number of students from different departments in an engineering college for the year $2012$. The proportion of male to female students in each department is $5:4$. There are $40$ males in Electrical Engineering. What is the difference between the numbers of female students in the Civil department and the female students in the Mechanical department?</p>
<p><img alt="" src="http://ee.gateoverflow.in//?qa=blob&qa_blobid=10534878894697419669"></p>Probability & Statisticshttps://ee.gateoverflow.in/348/gate2015-1-ga-8Sat, 11 Feb 2017 23:12:47 +0000GATE2015-1-GA-5
https://ee.gateoverflow.in/345/gate2015-1-ga-5
<p>Given set $A=\left\{ 2, 3, 4, 5\right\}$ and set $B=\left\{ 11, 12, 13, 14, 15\right\}$, two numbers are randomly selected, one from each set. What is the probability that the sum of two numbers equal $16$?</p>
<ol style="list-style-type:upper-alpha">
<li>$0.20$</li>
<li>$0.25$</li>
<li>$0.30$</li>
<li>$0.33$</li>
</ol>Probability & Statisticshttps://ee.gateoverflow.in/345/gate2015-1-ga-5Sat, 11 Feb 2017 23:12:47 +0000GATE2015-1-GA-9
https://ee.gateoverflow.in/349/gate2015-1-ga-9
<p>The probabilities that a student passes in Mathematics, Physics, and Chemistry are $m, p,$ and $c$ respectively. Of these subjects, the student has $75$% chance of passing in at least one, a $50$% chance of passing in at least two and a $40$% chance of passing in exactly two. Following relations are drawn in $m, p, c$:</p>
<p>(I) $p + m + c = 27/20$</p>
<p>(II) $p + m + c = 13/20$</p>
<p>(III) $(p) \times (m) \times (c) = 1/10$</p>
<ol style="list-style-type:upper-alpha">
<li>Only relation $I$ is true.</li>
<li>Only relation $II$ is true.</li>
<li>Relations $II$ and $III$ are true.</li>
<li>Relations $I$ and $III$ are true.</li>
</ol>Probability & Statisticshttps://ee.gateoverflow.in/349/gate2015-1-ga-9Sat, 11 Feb 2017 23:12:47 +0000GATE2016-2-33
https://ee.gateoverflow.in/318/gate2016-2-33
<p>Let the probability density function of a random variable, $X$, be given as:</p>
<p>$f_{x}(x)=\frac{3}{2}e^{-3x}u(x)+ae^{4x}u(-x)$</p>
<p>where u(x) is the unit step function.</p>
<p>Then the value of 'a' and prob $\left\{X \leq 0\right\}$, respectively are </p>
<ol style="list-style-type:upper-alpha">
<li>$2, \frac{1}{2}$</li>
<li>$4, \frac{1}{2}$</li>
<li>$2, \frac{1}{4}$</li>
<li>$4, \frac{1}{4}$</li>
</ol>Probability & Statisticshttps://ee.gateoverflow.in/318/gate2016-2-33Sun, 29 Jan 2017 20:21:26 +0000GATE2016-2-GA-9
https://ee.gateoverflow.in/284/gate2016-2-ga-9
<p>Shaquille 'O' Neal is a $60$% career free throw shooter, meaning that he successfully makes $60$ free throws out of $100$ attempts on average. What is the probability that he will successfully make exactly $6$ free throws in $10$ attempts?</p>
<ol style="list-style-type:upper-alpha">
<li>$0.2508$</li>
<li>$0.2816$</li>
<li>$0.2934$</li>
<li>$0.6000$</li>
</ol>Probability & Statisticshttps://ee.gateoverflow.in/284/gate2016-2-ga-9Sun, 29 Jan 2017 20:20:38 +0000GATE2016-2-GA-6
https://ee.gateoverflow.in/281/gate2016-2-ga-6
<p>The following graph represents the installed capacity for cement production (in tonnes) and the actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a plant is defined as ratio of actual production of cement to installed capacity. A plant with installed capacity of at least $200$ tonnes is called a large plant and a plant with lesser capacity is called a small plant. The difference between total production of large plants and small plants, in tonnes is ____.</p>
<p><img alt="" src="http://ee.gateoverflow.in//?qa=blob&qa_blobid=6923616878834591217"></p>Probability & Statisticshttps://ee.gateoverflow.in/281/gate2016-2-ga-6Sun, 29 Jan 2017 20:20:38 +0000GATE2016-1-26
https://ee.gateoverflow.in/236/gate2016-1-26
Candidates were asked to come to an interview with $3$ pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all $3$ pens having the same colour is _________.Probability & Statisticshttps://ee.gateoverflow.in/236/gate2016-1-26Sun, 29 Jan 2017 20:16:13 +0000