Test: Random Variables


20 Questions MCQ Test GATE ECE (Electronics) 2023 Mock Test Series | Test: Random Variables


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Attempt Test: Random Variables | 20 questions in 60 minutes | Mock test for Electronics and Communication Engineering (ECE) preparation | Free important questions MCQ to study GATE ECE (Electronics) 2023 Mock Test Series for Electronics and Communication Engineering (ECE) Exam | Download free PDF with solutions
QUESTION: 1

The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.

Que : The probability that more than 3 cars will arrive during any 10 min period is

Solution:

QUESTION: 2

The number of cars arriving at ICICI bank drive-in window during 10-min period is Poisson random variable X with b = 2.

Que: The probability that no car will arrive is

Solution:

QUESTION: 3

The power reflected from an aircraft of complicated shape that is received by a radar can be described by an exponential random variable W. The density of W is

where W0 is the average amount of received power. The probability that the received power is larger than the power received on the average is

Solution:

QUESTION: 4

Delhi averages three murder per week and their occurrences follow a poission distribution

Que: The probability that there will be five or more murder in a given week is

Solution:

QUESTION: 5

Delhi averages three murder per week and their occurrences follow a poission distribution

Que: On the average, how many weeks a year can Delhi expect to have no murders ?

Solution:

average number of week, per year with no murder

QUESTION: 6

Delhi averages three murder per week and their occurrences follow a poission distribution.

Que:How many weeds per year (average) can the Delhi expect the number of murders per week to equal orexceed the average number per week ?

Solution:

 

Average number of weeks per year that number of murder exceeds the average

QUESTION: 7

A discrete random variable X has possible values x i = i2  i =1, 2, 3, 4 which occur with probabilities 0.4, 0.25, 0.15, 0.1,. The mean value 

Solution:

QUESTION: 8

The random variable X is defined by the density

The expected value of g(X)  = X3 is

Solution:

QUESTION: 9

The random variables X and Y have variances 0.2 and 0.5 respectively. Let Z= 5X-2Y. The variance of Z is?

Solution:

Var(X) = 0.2, Var(Y) = 0.5
Z = 5X – 2Y
Var(Z) = Var(5X-2Y)
           = Var(5X) + Var(2Y)
           = 25Var(X) + 4Var(Y)
Var(Z) = 7.

QUESTION: 10

The variance of random variable X is

Solution:

Solution= 

Variance of X is σx2=E[X2]- μx2

E(X2)=-∞ x2fx(x)dx=01  x2(x)3(1-x)2dx=1/10

σx2 =(1/10)-(1/4)2=3/80

hence option B would be the correct answer.

QUESTION: 11

A Random variable X is uniformly distributed on the interval (-5, 15). Another random variableY =  e -X/5 is formed. The value of E[Y ] is

Solution:

QUESTION: 12

A joint sample space for two random variable X and Y has four elements (1, 1), (2, 2), (3, 3) and (4, 4). Probabilities of these elements are 0.1, 0.35, 0.05 and 0.5 respectively.

Que: The probability of the event {X ≤ 2.5, Y ≤ 6} is

Solution:

QUESTION: 13

A joint sample space for two random variable X and Y has four elements (1, 1), (2, 2), (3, 3) and (4, 4). Probabilities of these elements are 0.1, 0.35, 0.05 and 0.5 respectively.

Que: The probability of the event {X ≤ 3} is

Solution:

= 0.1+ 0.35 + 0.05 = 0.5

QUESTION: 14

The statistically independent random variable X and Y have mean values .and  They have second moments    and  Consider a random variable W = 3X - Y.

Que: The mean value E [W] is

Solution:

QUESTION: 15

The statistically independent random variable X and Y have mean values  .and   They have second moments    and   Consider a random variable W = 3X - Y.

Que: The second moment of W is

Solution:

QUESTION: 16

The statistically independent random variable X and Y have mean values  .and   They have second moments    and   Consider a random variable W = 3X - Y.

Que: The variance of the random variable is

Solution:

QUESTION: 17

Two random variable X and Y have the density function

The X and Y are

Solution:

QUESTION: 18

The value of σx2 , σy2 , RXY and ρ are respectively

Solution:

QUESTION: 19

The mean value of the random variable

W = (X + 3Y)2  + 2X + 3  is

Solution:

QUESTION: 20

If machine is not properly adjusted, the product resistance change to the case where ax = 1050Ω . Now the rejected fraction is

Solution:

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