1
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.
2
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 ______.
3
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 ______

4
GATE CSE 2020
Numerical
+2
-0.67
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 _______.