Recent questions tagged engineering-mathematics / GATE Overflow for GATE CSE

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331

Probability - Gravner-68.d
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of that student' ... of the randomly chosen group. Let EY= $\mu$ and Var(Y) = $\sigma$2 . Express EX with s, n, $\mu$ and $\sigma$.

Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. Firs...

Pooja Khatri

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Pooja Khatri asked Sep 25, 2018

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332

Probability - Gravner-68.c
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of that student's group . Next, choose one the four groups at random and let $Y$ be its size. (c) Compute Var(X) and Var(Y).

Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. Firs...

Pooja Khatri

291 views

Pooja Khatri asked Sep 25, 2018

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333

Probability - Gravner-68.b
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of that student's group . Next, choose one the four groups at random and let $Y$ be its size. (b) Compute EX and EY.

Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. Firs...

Pooja Khatri

162 views

Pooja Khatri asked Sep 25, 2018

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334

Probability - Gravner-68.a
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of ... , choose one the four groups at random and let $Y$ be its size. (a) Write down the probability mass functions for $X$ and $Y$.

Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. Firs...

Pooja Khatri

171 views

Pooja Khatri asked Sep 25, 2018

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335

Probability - Gravner-67.a
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number of times the two dice have to be rolled before the game is decided. (a)Determine the probability mass function of N.

You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number ...

Pooja Khatri

343 views

Pooja Khatri asked Sep 25, 2018

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336

Probability - Gravner-67.c
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number of times the two dice have to be rolled before the game is ... dollar for winning in the first round, 1 dollar for winning in any other round, and nothing otherwise.Compute your expected winnings .

You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number ...

Pooja Khatri

399 views

Pooja Khatri asked Sep 25, 2018

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337

Probability - Gravner-67.b
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number of times the two dice have to be rolled before the game is decided. (b) Compute Probability you win

You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number ...

Pooja Khatri

502 views

Pooja Khatri asked Sep 25, 2018

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338

Probability - Gravner-66
You are dealt one card at random form a full deck and your opponent is dealt $2$ cards (Without any replacement ). If you get an Ace, he pays you $10$ dollar, if you get a King, he pays you $5$ dollar (regardless of his cards). If you have ... red cards, he pays you $1$ dollar. In all other cases you pay him $1$ dollar . Determine your expected earnings . Are they positive?

You are dealt one card at random form a full deck and your opponent is dealt $2$ cards (Without any replacement ). If you get an Ace, he pays you $10$ dollar, if you get ...

Pooja Khatri

362 views

Pooja Khatri asked Sep 25, 2018

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339

Probability - Gravner-65.d
A biologist needs at least $3$ mature specimens of certain plant. The plant needs a year to reach maturity; once a seed is planted, any plant will survive for the year with probability $1/1000$ (independently of other plants). The biologist plants $3000$ ... the biologist should plant in order to get at least $3$ mature plants in a year with probability at least $0.999$.

A biologist needs at least $3$ mature specimens of certain plant. The plant needs a year to reach maturity; once a seed is planted, any plant will survive for the year wi...

Pooja Khatri

327 views

Pooja Khatri asked Sep 25, 2018

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340

Probability - Gravner-65.b
A biologist needs at least $3$ mature specimens of certain plant. The plant needs a year to reach maturity; once a seed is planted, any plant will survive for the year with probability $1/1000$ (independently of other plants). The ... these seeds reach maturity. (b) Write down a relevant approximate expression for the probability from(a).Justify briefly the approximation.

A biologist needs at least $3$ mature specimens of certain plant. The plant needs a year to reach maturity; once a seed is planted, any plant will survive for the year wi...

Pooja Khatri

176 views

Pooja Khatri asked Sep 25, 2018

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341

Probability - Gravner-65.a
A biologist needs at least $3$ mature specimens of certain plant. The plant needs a year to reach maturity; once a seed is planted, any plant will survive for the year with probability $1/1000$ (independently of other plants). The biologist ... ) Write down the exact expression for the probability that the biologist will indeed end up with at least $3$ mature plants.

A biologist needs at least $3$ mature specimens of certain plant. The plant needs a year to reach maturity; once a seed is planted, any plant will survive for the year wi...

Pooja Khatri

211 views

Pooja Khatri asked Sep 25, 2018

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342

Probability - Gravner-64.d
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (d) Find an expression for $P(Y>10)$.

Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(d) Find an expression for $P(Y>10)$.

Pooja Khatri

339 views

Pooja Khatri asked Sep 25, 2018

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343

Probability - Gravner-64.c
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (c) Find an expression $P$($X\geqslant 6$).

Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(c) Find an expression $P$($X\geqslant 6$)...

Pooja Khatri

170 views

Pooja Khatri asked Sep 25, 2018

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344

Probability - Gravner-64.b
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (b) Write down the probability mass function of Y.

Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(b) Write down the probability mass functi...

Pooja Khatri

287 views

Pooja Khatri asked Sep 25, 2018

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345

Probability - Gravner-64.a
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (a) Write down the probability mass function of X.

Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(a) Write down the probability mass functi...

Pooja Khatri

571 views

Pooja Khatri asked Sep 25, 2018

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346

Probability - Gravner-63
You roll a die, your opponent tosses a coin. If you roll $6$ you win; if you do not roll $6$ and your opponent tosses Heads you lose; otherwise, this round ends and the game repeats. On the average, how many rounds does the game last?

You roll a die, your opponent tosses a coin. If you roll $6$ you win; if you do not roll $6$ and your opponent tosses Heads you lose; otherwise, this round ends and the ...

Pooja Khatri

304 views

Pooja Khatri asked Sep 25, 2018

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347

Probability - Gravner-62
Assume a crime has been committed. It is known that the particular has certain characteristics, which occur with a small frequency $p$ (say,10-8) in a population of size $n$ say (108). A person who matches these characteristics has been found at random( ... security ) and , since $p$ is so small charged with the crime. There is no other evidence. What should the defense be?

Assume a crime has been committed. It is known that the particular has certain characteristics, which occur with a small frequency $p$ (say,10-8) in a population of size ...

Pooja Khatri

114 views

Pooja Khatri asked Sep 25, 2018

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348

Probability - Gravner-61
Suppose that the probability that a person is killed by lighting in a year is, independently, $1/(500)$ million. Assume that the US population is $300$ million.

Suppose that the probability that a person is killed by lighting in a year is, independently, $1/(500)$ million. Assume that the US population is $300$ million.

Pooja Khatri

157 views

Pooja Khatri asked Sep 25, 2018

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349

Probability - Gravner-60
Denote by $d$ the dominant gene and by $r$ the recessive gene at a single locus. Then $dd$ is called the pure dominant genotype, $dr$ is called hybrid, and $rr$ the pure recessive genotype. The two genotypes with at least one dominant gene, $dd$ and $dr$, result in the phenotype of the dominant gene, while $rr$ results in a recessive phenotype.

Denote by $d$ the dominant gene and by $r$ the recessive gene at a single locus. Then $dd$ is called the pure dominant genotype, $dr$ is called hybrid, and $rr$ the pure ...

Pooja Khatri

138 views

Pooja Khatri asked Sep 25, 2018

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350

Probability - Gravner-59
Let $X$ be the number shown on a rolled fair die. Compute EX,E(X2), and Var(X).

Let $X$ be the number shown on a rolled fair die. Compute EX,E(X2), and Var(X).

Pooja Khatri

148 views

Pooja Khatri asked Sep 25, 2018

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1 answer

351

Probablity-Gravner-58
Let $X$ be a random variable with $P(X=1) =0.2,P(X=2)=0.3$, and $P(X=3)=0.5$. What is the expected value of $X$?

Let $X$ be a random variable with $P(X=1) =0.2,P(X=2)=0.3$, and $P(X=3)=0.5$. What is the expected value of $X$?

Pooja Khatri

280 views

Pooja Khatri asked Sep 25, 2018

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1 answer

352

Probability - Gravner-56
Let $X$ be a random variable with $P(X=1) =0.2, P(X=2) = 0.3$, and $P(X=3) = 0.5$. What is the expected value of $X$?

Let $X$ be a random variable with $P(X=1) =0.2, P(X=2) = 0.3$, and $P(X=3) = 0.5$. What is the expected value of $X$?

Pooja Khatri

224 views

Pooja Khatri asked Sep 24, 2018

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353

Probability - Gravner-57
An urn contains $11$ balls, $3$ white , $3$ red, and $5$ blue balls. Take out $3$ balls at random, without replacement. You win $1$ for each red ball you select and lose a $1$ for each white ball you select. Determine the p.m.f. of $X$ , the amount you win.

An urn contains $11$ balls, $3$ white , $3$ red, and $5$ blue balls. Take out $3$ balls at random, without replacement. You win $1$ for each red ball you select and lose ...

Pooja Khatri

221 views

Pooja Khatri asked Sep 24, 2018

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354

Probability - Gravner-55
An urn contains $20$ balls numbers $1,.........20$. Select $5$ balls at random, without replacement. Let X be the largest number among selected balls. Determine its p.m.f. and the probability that at least one the selected numbers is $15$ or more.

An urn contains $20$ balls numbers $1,.........20$. Select $5$ balls at random, without replacement. Let X be the largest number among selected balls. Determine its p.m.f...

Pooja Khatri

153 views

Pooja Khatri asked Sep 24, 2018

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1 answer

355

Probability - Gravner-54
Let $X$ be the number of Heads in $2$ fair coin tosses. Determine its p.m.f.

Let $X$ be the number of Heads in $2$ fair coin tosses. Determine its p.m.f.

Pooja Khatri

235 views

Pooja Khatri asked Sep 24, 2018

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356

Probability - Gravner-53.b
Consider the following game. A player rolls a die. If he rolls $3$ or less, he loses immediately. Otherwise he selects, at random, as many cards from a full deck as the number that came up on the die. The player wins if all four Aces are among the ... ) Smith tells you that he recently played this game once and won. That is the probability that he rolled a $6$ on the die?

Consider the following game. A player rolls a die. If he rolls $3$ or less, he loses immediately. Otherwise he selects, at random, as many cards from a full deck as the n...

Pooja Khatri

240 views

Pooja Khatri asked Sep 24, 2018

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357

Probability - Gravner-53.a
Consider the following game. A player rolls a die. If he rolls $3$ or less, he loses immediately. Otherwise he selects, at random, as many cards from a full deck as the number that came up on the die. The player wins if all four Aces are among the selected cards. (a) Compute the winning probability for this game.

Consider the following game. A player rolls a die. If he rolls $3$ or less, he loses immediately. Otherwise he selects, at random, as many cards from a full deck as the n...

Pooja Khatri

216 views

Pooja Khatri asked Sep 24, 2018

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358

Probability - Gravner-52.b
Five married couples are seated at random around a round table. (b) Compute the probability that at most one wife does not sit next to her husband.

Five married couples are seated at random around a round table.(b) Compute the probability that at most one wife does not sit next to her husband.

Pooja Khatri

99 views

Pooja Khatri asked Sep 24, 2018

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359

Probability - Gravner-52.a
Five married couples are seated at random around a round table. (a) Compute the probability that all couples sit together(i.e., every husband-wife pair occupies adjacent seats).

Five married couples are seated at random around a round table.(a) Compute the probability that all couples sit together(i.e., every husband-wife pair occupies adjacent s...

Pooja Khatri

171 views

Pooja Khatri asked Sep 24, 2018

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360

Probability - Gravner-51.b
Ten fair dice are rolled. What is the probability that: (b) Each of the number $1,2,3$ appears exactly twice, while the number $4$ appears four times.

Ten fair dice are rolled. What is the probability that:(b) Each of the number $1,2,3$ appears exactly twice, while the number $4$ appears four times.

Pooja Khatri

124 views

Pooja Khatri asked Sep 24, 2018

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