1
GATE CSE 2023
MCQ (More than One Correct Answer)
+2
-0.67

Consider a random experiment where two fair coins are tossed. Let A be the event that denotes HEAD on both the throws, B be the event that denotes HEAD on the first throw, and C be the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?

A
A and B are independent
B
A and C are independent
C
B and C are independent
D
Prob(B|C) = Prob(B)
2
GATE CSE 2021 Set 1
+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?

A
S1 is false, but S2 is true.
B
S1 is true, but S2 is false.
C

Both S1 and S2 are true.

D
Both S1 and S2 are false.
3
GATE CSE 2021 Set 1
Numerical
+2
-0.67
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 ______.
4
GATE CSE 2021 Set 1
Numerical
+2
-0.67

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 ______

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