GATE Overflow for GATE CSE - Recent questions tagged binomial-distribution
https://gateoverflow.in/tag/binomial-distribution
Powered by Question2AnswerBest Open Video Playlist for Binomial Distributions Topic | Probability
https://gateoverflow.in/380548/video-playlist-binomial-distributions-topic-probability
<p>Please list out the best free available video playlist for Binomial Distributions Topic from Probability as an answer here (only one playlist per answer). We'll then select the best playlist and add to <a href="http://classroom.gateoverflow.in" rel="nofollow">GO classroom</a> video lists. You can add any video playlist link including your own (as long as they are free to access) but standard ones are more likely to be selected as best.<br>
<br>
For the full list of selected videos please see <a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQTEfCg28q1B_buKRxaVvUjN_CTu9UntAiqi9qBiZZesmJE6LnqfkuwxNQOsNcU1g/pubhtml" rel="nofollow">here</a></p>Study Resourceshttps://gateoverflow.in/380548/video-playlist-binomial-distributions-topic-probabilityMon, 15 Aug 2022 11:20:30 +0000MadeEasy Test Series: Probability
https://gateoverflow.in/291812/madeeasy-test-series-probability
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=1245297611636610759"></p>
<hr>
<p>How to get the idea that we have to use Binomial distribution or Hypergeometric Distribution.</p>
<p>I know that if the probability is not changing(i.e with replacement) then we go Binomial otherwise Hypergeometric. But in question, it is not indicating anything about a replacement.</p>
<p>So is there any by default approach that we have to use Binomial if nothing is a mention about a replacement.</p>Mathematical Logichttps://gateoverflow.in/291812/madeeasy-test-series-probabilityWed, 09 Jan 2019 09:01:59 +0000Binomial distribution
https://gateoverflow.in/280676/binomial-distribution
Is there any relation between MEAN, VARIANCE and MODE for binomial distribution?<br />
<br />
Let, Mean = 8, variance = 6 for any binomial distribution.<br />
<br />
np = 8 and npq = 6 => q=$3/4$, p=$1/4$<br />
<br />
Now is there any relation to find value of MODE ?Mathematical Logichttps://gateoverflow.in/280676/binomial-distributionTue, 18 Dec 2018 16:32:15 +0000Hk Dass
https://gateoverflow.in/238650/hk-dass
In a binomial distribution the sum and the product of mean and variance are $\Large \frac{25}{3}$ and $\Large \frac{50}{3}$ respectively. The distribution is _______.<br />
<br />
Note : I've not included the options to avoid KBC in commentsProbabilityhttps://gateoverflow.in/238650/hk-dassFri, 31 Aug 2018 05:14:09 +0000Probability
https://gateoverflow.in/231999/probability
<p>We have applied Bernoulli equation to solve the answer.</p>
<p>But, why the answer isn't C(90,5)÷C(100,5)?</p>
<p> </p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=935211936145362436"></p>Probabilityhttps://gateoverflow.in/231999/probabilityThu, 09 Aug 2018 06:57:39 +0000TIFR CSE 2018 | Part A | Question: 10
https://gateoverflow.in/179279/tifr-cse-2018-part-a-question-10
<p>Let $C$ be a biased coin such that the probability of a head turning up is $p.$ Let $p_n$ denote the probability that an odd number of heads occurs after $n$ tosses for $n \in \{0,1,2,\ldots \},$ Then which of the following is TRUE ?</p>
<ol style="list-style-type:upper-alpha">
<li>$p_n=\dfrac{1}{2}\text{ for all }n \in \{0,1,2,\ldots \}.$</li>
<li>$p_n=(1-p)(1-p_{n-1})+p.p_{n-1}\text{ for }n\geq 1\text{ and }p_{0}=0.$</li>
<li>$p_{n}=\sum_ {i=1}^{n}p(1-2p)^{i-1} \text{ for }n\geq 1.$</li>
<li>$\text{If } p=\dfrac{1}{2},\text{ then } p_{n}=\dfrac{1}{2} \text{ for all }n \in \{0,1,2,\ldots\}$.</li>
<li>$p_{n}=1 \text{ if } n \text{ is odd and } 0 \text{ otherwise}.$</li>
</ol>Probabilityhttps://gateoverflow.in/179279/tifr-cse-2018-part-a-question-10Sun, 10 Dec 2017 01:38:13 +0000$a_n = 4^n + 6^n$
https://gateoverflow.in/130200/%24a_n-4-n-6-n%24
If $a_n = 4^n + 6^n$ Find the value of $a_{40} \text { mod } 25$Set Theory & Algebrahttps://gateoverflow.in/130200/%24a_n-4-n-6-n%24Fri, 19 May 2017 14:22:44 +0000Hashing+Probaility
https://gateoverflow.in/72537/hashing-probaility
<p><img alt="Loading Question" src="https://d2190hpfa85jkd.cloudfront.net/q/db8e79d6199d17a32b5e00d4971535bb.jpg"></p>DShttps://gateoverflow.in/72537/hashing-probailitySat, 08 Oct 2016 11:35:59 +0000TIFR CSE 2013 | Part A | Question: 14
https://gateoverflow.in/25437/tifr-cse-2013-part-a-question-14
<p>An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$\dfrac{1}{(2n)}$</li>
<li>$\dfrac{1}{[(6n)!]}$</li>
<li>$1 - 6^{-n}$</li>
<li>$6^{-n}$</li>
<li>None of the above</li>
</ol>Probabilityhttps://gateoverflow.in/25437/tifr-cse-2013-part-a-question-14Wed, 04 Nov 2015 14:24:17 +0000TIFR CSE 2013 | Part A | Question: 4
https://gateoverflow.in/25386/tifr-cse-2013-part-a-question-4
<p>A biased coin is tossed repeatedly. Assume that the outcomes of different tosses are independent and probability of heads is $\dfrac{2}{3}$ in each toss. What is the probability of obtaining an even number of heads in $5$ tosses, zero being treated as an even number?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$\left(\dfrac{121}{243}\right)$</li>
<li>$\left(\dfrac{122}{243}\right)$</li>
<li>$\left(\dfrac{124}{243}\right)$</li>
<li>$\left(\dfrac{125}{243}\right)$</li>
<li>$\left(\dfrac{128}{243}\right)$</li>
</ol>Probabilityhttps://gateoverflow.in/25386/tifr-cse-2013-part-a-question-4Wed, 04 Nov 2015 07:51:58 +0000TIFR CSE 2012 | Part A | Question: 17
https://gateoverflow.in/25042/tifr-cse-2012-part-a-question-17
<p>A spider is at the bottom of a cliff, and is $n$ inches from the top. Every step it takes brings it one inch closer to the top with probability $1/3$, and one inch away from the top with probability $2/3$, unless it is at the bottom in which case, it always gets one inch closer. What is the expected number of steps for the spider to reach the top as a function of $n$?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>It will never reach the top.</li>
<li>Linear in $n$.</li>
<li>Polynomial in $n$.</li>
<li>Exponential in $n$.</li>
<li>Double exponential in $n$.</li>
</ol>Probabilityhttps://gateoverflow.in/25042/tifr-cse-2012-part-a-question-17Fri, 30 Oct 2015 13:39:59 +0000TIFR CSE 2011 | Part A | Question: 3
https://gateoverflow.in/20000/tifr-cse-2011-part-a-question-3
<p>The probability of three consecutive heads in four tosses of a fair coin is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$\left(\dfrac{1}{4}\right)$</li>
<li>$\left(\dfrac{1}{8}\right)$</li>
<li>$\left(\dfrac{1}{16}\right)$</li>
<li>$\left(\dfrac{3}{16}\right)$</li>
<li>None of the above</li>
</ol>Probabilityhttps://gateoverflow.in/20000/tifr-cse-2011-part-a-question-3Sat, 17 Oct 2015 07:31:18 +0000TIFR CSE 2010 | Part B | Question: 38
https://gateoverflow.in/19050/tifr-cse-2010-part-b-question-38
<p>Suppose three coins are lying on a table, two of them with heads facing up and one with tails facing up. One coin is chosen at random and flipped. What is the probability that after the flip the majority of the coins(i.e., at least two of them) will have heads facing up?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$\left(\frac{1}{3}\right)$</li>
<li>$\left(\frac{1}{8}\right)$</li>
<li>$\left(\frac{1}{4}\right)$</li>
<li>$\left(\frac{1}{4}+\frac{1}{8}\right)$</li>
<li>$\left(\frac{2}{3}\right)$</li>
</ol>Probabilityhttps://gateoverflow.in/19050/tifr-cse-2010-part-b-question-38Sat, 10 Oct 2015 19:36:00 +0000TIFR CSE 2010 | Part A | Question: 6
https://gateoverflow.in/18222/tifr-cse-2010-part-a-question-6
<p>Given 10 tosses of a coin with probability of head = .$4$ = ($1$ - the probability of tail), the probability of at least one head is?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$(.4)^{10}$</li>
<li>$1 - (.4)^{10}$</li>
<li>$1 - (.6)^{10}$</li>
<li>$(.6)^{10}$</li>
<li>$10(.4) (.6)^{9}$</li>
</ol>Probabilityhttps://gateoverflow.in/18222/tifr-cse-2010-part-a-question-6Fri, 02 Oct 2015 01:53:28 +0000GATE IT 2005 | Question: 32
https://gateoverflow.in/3778/gate-it-2005-question-32
<p>An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is</p>
<ol style="list-style-type:upper-alpha">
<li>$3$</li>
<li>$4$</li>
<li>$5$</li>
<li>$6$</li>
</ol>Probabilityhttps://gateoverflow.in/3778/gate-it-2005-question-32Mon, 03 Nov 2014 08:48:29 +0000GATE IT 2006 | Question: 22
https://gateoverflow.in/3561/gate-it-2006-question-22
<p>When a coin is tossed, the probability of getting a Head is $p, 0 < p < 1$. Let $N$ be the random variable denoting the number of tosses till the first Head appears, including the toss where the Head appears. Assuming that successive tosses are independent, the expected value of $N$ is</p>
<ol style="list-style-type:upper-alpha">
<li>$\dfrac{1}{p}$</li>
<li>$\dfrac{1}{(1 - p)}$</li>
<li>$\dfrac{1}{p^{2}}$</li>
<li>$\dfrac{1}{(1 - p^{2})}$</li>
</ol>Probabilityhttps://gateoverflow.in/3561/gate-it-2006-question-22Fri, 31 Oct 2014 03:26:45 +0000GATE IT 2007 | Question: 1
https://gateoverflow.in/3432/gate-it-2007-question-1
<p>Suppose there are two coins. The first coin gives heads with probability $\dfrac{5}{8}$ when tossed, while the second coin gives heads with probability $\dfrac{1}{4}.$ One of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads ?</p>
<ol style="list-style-type:upper-alpha">
<li>$\left(\dfrac{7}{8}\right)$</li>
<li>$\left(\dfrac{1}{2}\right)$</li>
<li>$\left(\dfrac{7}{16}\right)$</li>
<li>$\left(\dfrac{5}{32}\right)$</li>
</ol>Probabilityhttps://gateoverflow.in/3432/gate-it-2007-question-1Wed, 29 Oct 2014 20:42:23 +0000GATE CSE 2005 | Question: 52
https://gateoverflow.in/1177/gate-cse-2005-question-52
<p>A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is:</p>
<ol style="list-style-type: upper-alpha;">
<li>$\frac{1}{2^n}$</li>
<li>$1 - \frac{1}{n}$</li>
<li>$\frac{1}{n!}$</li>
<li>$1 - \frac{1}{2^n}$</li>
</ol>Probabilityhttps://gateoverflow.in/1177/gate-cse-2005-question-52Sun, 21 Sep 2014 06:31:25 +0000GATE CSE 2006 | Question: 21
https://gateoverflow.in/982/gate-cse-2006-question-21
<p>For each element in a set of size $2n$, an unbiased coin is tossed. The $2n$ coin tosses are independent. An element is chosen if the corresponding coin toss was a head. The probability that exactly $n$ elements are chosen is</p>
<ol style="list-style-type: upper-alpha;">
<li>$\frac{^{2n}\mathrm{C}_n}{4^n}$</li>
<li>$\frac{^{2n}\mathrm{C}_n}{2^n}$</li>
<li>$\frac{1}{^{2n}\mathrm{C}_n}$</li>
<li>$\frac{1}{2}$</li>
</ol>Probabilityhttps://gateoverflow.in/982/gate-cse-2006-question-21Wed, 17 Sep 2014 12:33:42 +0000GATE CSE 2002 | Question: 2.16
https://gateoverflow.in/846/gate-cse-2002-question-2-16
<p>Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$\frac{1}{16}$</li>
<li>$\frac{1}{8}$</li>
<li>$\frac{7}{8}$</li>
<li>$\frac{15}{16}$</li>
</ol>Probabilityhttps://gateoverflow.in/846/gate-cse-2002-question-2-16Mon, 15 Sep 2014 18:54:10 +0000