Search results for random-variable / GATE Overflow for GATE CSE

50 votes

7 answers

1

GATE CSE 2017 Set 2 | Question: 31
For any discrete random variable $X$, with probability mass function $P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For a certain ... . The expectation of $Y$ is $N \beta(1-\beta)$ $N \beta$ $N (1-\beta)$ Not expressible in terms of $N$ and $\beta$ alone

For any discrete random variable $X$, with probability mass function$P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomi...

Arjun

16.1k views

Arjun asked Feb 14, 2017

52 votes

3 answers

2

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

41 votes

4 answers

3

GATE CSE 2012 | Question: 21
Consider a random variable $X$ that takes values $+1$ and $−1$ with probability $0.5$ each. The values of the cumulative distribution function $F(x)$ at $x = −1$ and $+1$ are $0$ and $0.5$ $0$ and $1$ $0.5$ and $1$ $0.25$ and $0.75$

Consider a random variable $X$ that takes values $+1$ and $−1$ with probability $0.5$ each. The values of the cumulative distribution function $F(x)$ at $x = −1$ and ...

Arjun

12.7k views

Arjun asked Sep 24, 2014

2 votes

3 answers

4

GATE CSE 2024 | Set 2 | Question: 34
Let $x$ and $y$ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $z=x y$ and let the mean values of $x, y, z$ be $\bar{x}, \bar{y}, \bar{z}$ ... $\bar{z} \leq \bar{x} \bar{y}$ $\bar{z} \geq \bar{x} \bar{y}$ $\bar{z} \leq \bar{x}$

Let $x$ and $y$ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $z=x y$ and let the mean values of $x, y, z$ be $\bar...

Arjun

2.7k views

Arjun asked Feb 16

55 votes

6 answers

5

GATE CSE 2015 Set 3 | Question: 37
Suppose $X_i$ for $i=1, 2, 3$ are independent and identically distributed random variables whose probability mass functions are $Pr[X_i = 0] = Pr[X_i = 1] = \frac{1} {2} \text{ for } i = 1, 2, 3$. Define another random variable $Y = X_1X_2 \oplus X_3$, where $\oplus$ denotes XOR. Then $Pr[Y=0 \mid X_3 = 0] =$______.

Suppose $X_i$ for $i=1, 2, 3$ are independent and identically distributed random variables whose probability mass functions are $Pr[X_i = 0] = Pr[X_i = 1] = \frac{1} {2} ...

go_editor

18.5k views

go_editor asked Feb 15, 2015

36 votes

7 answers

6

GATE CSE 2011 | Question: 18
If the difference between the expectation of the square of a random variable $\left(E\left[X^2\right]\right)$ and the square of the expectation of the random variable $\left(E\left[X\right]\right)^2$ is denoted by $R$, then $R=0$ $R<0$ $R\geq 0$ $R > 0$

If the difference between the expectation of the square of a random variable $\left(E\left[X^2\right]\right)$ and the square of the expectation of the random variable $\l...

go_editor

9.0k views

go_editor asked Sep 29, 2014

1 votes

1 answer

7

GATE DS&AI 2024 | Question: 47
Let $X$ be a random variable exponentially distributed with parameter $\lambda>0$. The probability density function of $X$ is given by: \[ f_{X}(x)=\left\{\begin{array}{ll} \lambda e^{-\lambda x}, \quad x \geq 0 \\ 0, & \text { otherwise } \end ... variance of $X$, respectively, the value of $\lambda$ is $\_\_\_\_\_\_\_\_$ (rounded off to one decimal place).

Let $X$ be a random variable exponentially distributed with parameter $\lambda>0$. The probability density function of $X$ is given by:\[f_{X}(x)=\left\{\begin{array}{ll}...

Arjun

696 views

Arjun asked Feb 16

6 votes

1 answer

8

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 12
Let $x$ be a random variable possessing the probability density function $ f(x)= \begin{cases}c x & , x \in[0,10] \\ 0 & , \text { otherwise }\end{cases} $ where $c \in \mathbb{R}$. The probability that $x \in[1,2]$ is ______. $\dfrac{1}{100}$ $\dfrac{3}{100}$ $\dfrac{5}{100}$ $\dfrac{7}{100}$

Let $x$ be a random variable possessing the probability density function$$f(x)= \begin{cases}c x & , x \in[0,10] \\ 0 & , \text { otherwise }\end{cases}$$where $c \in \ma...

GO Classes

496 views

GO Classes asked Jan 28

3 votes

1 answer

9

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 28
Suppose that $X$ and $Y$ are independent random variables such that each is equal to $0$ with probability $.5$ and $1$ with probability $.5.$ Find $P(X+Y \leq 1)?$ (Answer up to $2$ decimals)

Suppose that $X$ and $Y$ are independent random variables such that each is equal to $0$ with probability $.5$ and $1$ with probability $.5.$Find $P(X+Y \leq 1)?$ (Answe...

GO Classes

531 views

GO Classes asked Jan 13

0 votes

1 answer

10

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

310 views

GO Classes asked Feb 4

0 votes

1 answer

11

A simple random sample of 100 observations was taken from a large population. The sample mean and standard deviation were determined to be 80 and 12 respectively. The standard error of mean is ____________

Gaurav Kadyan

487 views

Gaurav Kadyan asked Sep 27, 2023

0 votes

1 answer

12

Probability | Bivariate Random Distribution

Debargha Mitra Roy

213 views

Debargha Mitra Roy asked Sep 20, 2023

16 votes

2 answers

13

GATE CSE 2021 Set 1 | Question: 18
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.

The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly pick...

Arjun

9.4k views

Arjun asked Feb 18, 2021

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