Search results for distribution / GATE Overflow for GATE CSE

74 votes

8 answers

1

GATE IT 2005 | Question: 32
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 $3$ $4$ $5$ $6$

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$3...

Ishrat Jahan

33.1k views

Ishrat Jahan asked Nov 3, 2014

33 votes

4 answers

2

GATE CSE 2019 | Question: 47
Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only real roots is (rounded off to $1$ decimal place) _______

Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only real roots is (rounded off to $1$ decimal...

Arjun

16.3k views

Arjun asked Feb 7, 2019

48 votes

5 answers

3

GATE CSE 2017 Set 1 | Question: 19
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ and $b$. The median of $Y$ is ______________ .

Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ ...

Arjun

20.6k views

Arjun asked Feb 14, 2017

52 votes

3 answers

4

GATE CSE 2008 | Question: 29
Let $X$ be a random variable following normal distribution with mean $+1$ and variance $4$. Let $Y$ be another normal variable with mean $-1$ and variance unknown. If $P (X \leq -1) = P (Y \geq 2)$ , the standard deviation of $Y$ is $3$ $2$ $\sqrt{2}$ $1$

Let $X$ be a random variable following normal distribution with mean $+1$ and variance $4$. Let $Y$ be another normal variable with mean $-1$ and variance unknown. If $P ...

Kathleen

23.7k views

Kathleen asked Sep 11, 2014

61 votes

3 answers

5

GATE CSE 2014 Set 1 | Question: 2
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .

Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .

Arjun

17.5k views

Arjun asked Sep 26, 2014

2 votes

1 answer

6

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 48
Consider the quadratic equation $x^2+\dfrac{x}{2}+c=0$, where $c$ is chosen uniformly randomly from the interval $[0,1]$. What is the probability that the given quadratic equation has a real solution? The solutions of $a x^2+b x+c=0$ are given by $x=\dfrac{-b \pm \sqrt{b^2-4 a c}}{2a}$. $1 / 2$ $1 / 4$ $1 / 8$ $1 / 16$

Consider the quadratic equation $x^2+\dfrac{x}{2}+c=0$, where $c$ is chosen uniformly randomly from the interval $[0,1]$. What is the probability that the given quadratic...

GO Classes

381 views

GO Classes asked Feb 5

0 votes

1 answer

7

Memory Based GATE DA 2024 | Question: 42
Consider two random variables, (x) and (y), each following a uniform distribution. Specifically, (x) is uniformly distributed over the interval ([1, 3]), and (y) is uniformly distributed over the interval ([2, 4]). What will be $P(x \geq y)$

Consider two random variables, (x) and (y), each following a uniform distribution. Specifically, (x) is uniformly distributed over the interval ([1, 3]), and (y) is uni...

GO Classes

308 views

GO Classes asked Feb 4

27 votes

11 answers

8

GATE CSE 2005 | Question: 52
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: $\frac{1}{2^n}$ $1 - \frac{1}{n}$ $\frac{1}{n!}$ $1 - \frac{1}{2^n}$

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 probabili...

gatecse

8.7k views

gatecse asked Sep 21, 2014

0 votes

0 answers

9

Memory Based GATE DA 2024 | Question: 11
Consider a dataset with a raw score $x = 75$, a mean $\mu = 70$, and a standard deviation $\sigma = 5$. Calculate the Z-score using the formula $z = \frac{x - \mu}{\sigma}$.

Consider a dataset with a raw score $x = 75$, a mean $\mu = 70$, and a standard deviation $\sigma = 5$. Calculate the Z-score using the formula \(z = \frac{x - \mu}...

GO Classes

195 views

GO Classes asked Feb 4

0 votes

0 answers

10

Memory Based GATE DA 2024 | Question: 44
Consider the statements below related to probability distributions: \textbf{(S1):} For a Poisson distribution, the mean and variance are equal. \textbf{(S2):} For a standard normal distribution, the mean is 0, and the variance is 1. Which of the following ... true. S1 is true, but S2 is false. S1 is false, but S2 is true. Both S1 and S2 are false.

Consider the statements below related to probability distributions:\textbf{(S1):} For a Poisson distribution, the mean and variance are equal.\textbf{(S2):} For a standar...

GO Classes

181 views

GO Classes asked Feb 4

43 votes

3 answers

11

GATE IT 2007 | Question: 57
In a multi-user operating system on an average, $20$ requests are made to use a particular resource per hour. The arrival of requests follows a Poisson distribution. The probability that either one, three or five requests are made in $45$ ... $6.9 \times 10^3 \times e^{-20}$ $1.02 \times 10^3 \times e^{-20}$

In a multi-user operating system on an average, $20$ requests are made to use a particular resource per hour. The arrival of requests follows a Poisson distribution. The ...

Ishrat Jahan

9.6k views

Ishrat Jahan asked Oct 30, 2014

43 votes

12 answers

12

GATE CSE 2007 | Question: 24
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these

Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier positio...

Kathleen

15.2k views

Kathleen asked Sep 21, 2014

24 votes

2 answers

13

GATE CSE 2020 | Question: 45
For $n>2$, let $a \in \{0,1\}^n$ be a non-zero vector. Suppose that $x$ is chosen uniformly at random from $\{0,1\}^n$. Then, the probability that $\displaystyle{} \Sigma_{i=1}^n a_i x_i$ is an odd number is______________

For $n>2$, let $a \in \{0,1\}^n$ be a non-zero vector. Suppose that $x$ is chosen uniformly at random from $\{0,1\}^n$. Then, the probability that $\displaystyle{} \Sigm...

Arjun

12.3k views

Arjun asked Feb 12, 2020

4 votes

0 answers

14

TIFR CSE 2023 | Part B | Question: 7
Consider the random variables $N, H$, and $T$ sampled as follows. First, $N$ is sampled from the Poisson$(10)$ distribution. This means that for each integer $n \geq 0$, \[ \operatorname{Pr}[N=n]=\frac{e^{-10} 10^{n}}{n !} \text {. } \] Then $N$ independent fair ... $E[H T]<E[H] \times E[T]$. $H$ and $T$ are not independent, and $E[H T]>E[H] \times E[T]$.

Consider the random variables $N, H$, and $T$ sampled as follows. First, $N$ is sampled from the Poisson$(10)$ distribution. This means that for each integer $n \geq 0$,\...

admin

587 views

admin asked Mar 14, 2023

35 votes

4 answers

15

GATE CSE 1998 | Question: 3a
Two friends agree to meet at a park with the following conditions. Each will reach the park between 4:00 pm and 5:00 pm and will see if the other has already arrived. If not, they will wait for 10 minutes or the end of the hour whichever is earlier and leave. What is the probability that the two will not meet?

Two friends agree to meet at a park with the following conditions. Each will reach the park between 4:00 pm and 5:00 pm and will see if the other has already arrived. If ...

Kathleen

6.3k views

Kathleen asked Sep 25, 2014

1 votes

1 answer

16

canvas
The weight of a light bulb has an average of 12.5 grs. with a standard deviation of 2. Assume the variable is normally distributed. If an inspector select randomly a sample of 30 bulbs ¿what is the probability of the weight of one bulb falls between 10 and 15 grs.?

The weight of a light bulb has an average of 12.5 grs. with a standard deviation of 2. Assume the variable is normally distributed. If an inspector select randomly a sa...

Ernestogld

746 views

Ernestogld asked Mar 10, 2023

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