1

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 ______.

Your input ____

2

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 ______

Your input ____

3

GATE CSE 2020

Numerical

+2

-0.67

For n > 2, let a {0, 1}

Then, the probability that $$\sum\limits_{i = 1}^n {{a_i}{x_i}} $$ is an odd number is _______.

^{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 _______.

Your input ____

4

GATE CSE 2019

Numerical

+2

-0.67

Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x

^{2}+ 6xY + 3Y + 6 has only real roots is (rounded off to 1 decimal place) _____.Your input ____

Questions Asked from Probability (Marks 2)

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