Electrical Engineering
GATE EE Probability and Statistics PYQs
Build your understanding with focused practice from past exam papers.
How to practice Probability and Statistics
Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.
Questions 1–10 of 16. Imported answers require independent review unless marked reviewed.
Question 64
Open questionEENAT2 marksNeeds review
Let X and Y be two real-valued random variables with E(X) = 1, E(Y) = 2, E(X²) = 4, E(Y²) = 9, and E(XY) = 0.9, where E denotes the expectation operator.
The value of α that minimizes E((X − αY)²) is __________ (Round off to one decimal place)
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Open questionEEMCQ1 markNeeds review
Consider discrete random variables
and
with probabilities as follows:
Given
, the expected value of
isYour answerChoose one option.
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Open questionEEMCQ2 marksNeeds review
Let
and
be continuous random variables with probability density functions
and
, respectively. Further, let
and
Which one of the following options is correct?
Your answerChoose one option.
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Open questionEEMSQ1 markNeeds review
Let
be a discrete random variable that is uniformly distributed over the set
. Which of the following random variables is/are uniformly distributed?Your answerSelect all correct options. You can choose more than one.
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Open questionEEMCQ1 markNeeds review
One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation
. The
is estimated by randomly drawing out 10,000 numbers of samples (
). The estimates
are computed in the following two ways.
Which of the following statements is true?
Your answerChoose one option.
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Open questionEENAT1 markNeeds review
Three points in the x-y plane are (-1, 0.8), (0, 2.2) and (1, 2.8). The value of the slope of the best fit straight line in the least square sense is __________ (Round off to 2 decimal places).
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Open questionEENAT2 marksNeeds review
The expected number of trials for first occurrence of a “head” in a biased coin is known to be 4. The probability of first occurrence of a “head” in the second trial is __________ (Round off to 3 decimal places).
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Open questionGAMCQ2 marksNeeds review
There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are equally likely.
The two dice are thrown once independently at random.
What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes: Q, U and V?
Your answerChoose one option.
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Open questionEENAT2 marksNeeds review
Let the probability density function of a random variable
be given as
The value of ‘a’ is ________.Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 8
Open questionGAMCQ2 marksNeeds review
Let
be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of
be
for
. The mean of
is ____Your answerChoose one option.
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