GATE ECE (Electronics) Test: Random Variables Free Online Test 2026
MCQ Practice Test & Solutions: Test: Random Variables (20 Questions)
You can prepare effectively for Electronics and Communication Engineering (ECE) GATE ECE (Electronics) Mock Test Series 2027 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Random Variables". These 20 questions have been designed by the experts with the latest curriculum of Electronics and Communication Engineering (ECE) 2026, to help you master the concept.
Test Highlights:
- - Format: Multiple Choice Questions (MCQ)
- - Duration: 60 minutes
- - Number of Questions: 20
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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
Detailed Solution: 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 no car will arrive is
Detailed Solution: Question 2
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
Detailed Solution: Question 3
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
Detailed Solution: Question 4
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 ?
Detailed Solution: Question 5
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 ?
Detailed Solution: Question 6
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 
Detailed Solution: Question 7
The random variable X is defined by the density
The expected value of g(X) = X3 is
Detailed Solution: Question 8
The random variables X and Y have variances 0.2 and 0.5 respectively. Let Z= 5X-2Y. The variance of Z is?
Detailed Solution: Question 9
The variance of the random variable X with probability density function 
is
isDetailed Solution: Question 10
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
Detailed Solution: Question 11
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
Detailed 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 ≤ 3} is
Detailed Solution: Question 13
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
.and They have second moments and Consider a random variable W = 3X - Y.Detailed Solution: 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 variance of the random variable is
.and They have second moments and Consider a random variable W = 3X - Y.Detailed Solution: Question 15
Two random variable X and Y have the density function
The X and Y are
Detailed Solution: Question 16
Detailed Solution: Question 17
The mean value of the random variable
W = (X + 3Y)2 + 2X + 3 is
Detailed Solution: Question 18
If machine is not properly adjusted, the product resistance change to the case where ax = 1050Ω. Now the rejected fraction is
Detailed Solution: Question 19
Suppose Y is a random variable representing the number of successes in 5 independent Bernoulli trials with success probability p = 0.6. What is the probability that Y equals 3?
Detailed Solution: Question 20
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