1
GATE CSE 2021 Set 1
MCQ (Single Correct Answer)
+2
-0.67
Consider the two statements.
S1 : There exist random variables X and Y such that
(E[X - E(X)) (Y - E(Y))])2 > Var[X] Var[Y]
S2 : For all random variables X and Y,
Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|]
Which one of the following choices is correct?
2
GATE CSE 2021 Set 1
Numerical
+2
-0
A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R).
In the graph below, the weight of edge (u, v) is the probability of receiving v when u is transmitted, where u, v ∈ {H, L}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7.
If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is ______
Your input ____
3
GATE CSE 2020
Numerical
+2
-0
For n > 2, let a {0, 1}n be a non-zero vector. Suppose that x is chosen uniformly at random from {0, 1}n.
Then, the probability that $$\sum\limits_{i = 1}^n {{a_i}{x_i}} $$ is an odd number is _______.
Then, the probability that $$\sum\limits_{i = 1}^n {{a_i}{x_i}} $$ is an odd number is _______.
Your input ____
4
GATE CSE 2019
Numerical
+2
-0
Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x2 + 6xY + 3Y + 6 has only real roots is (rounded off to 1 decimal place) _____.
Your input ____
Questions Asked from Probability (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
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