1
GATE CSE 2025 Set 1
Numerical
+2
-0

Consider a probability distribution given by the density function $P(x)$.

$$P(x)=\left\{\begin{array}{cc} C x^2, & \text { for } 1 \leq x \leq 4 \\ 0, & \text { for } x<1 \text { or } x>4 \end{array}\right.$$

The probability that $x$ lies between 2 and 3, i.e., $P(2 \leq x \leq 3)$ is _________ (Rounded off to three decimal places)

Your input ____
2
GATE CSE 2024 Set 2
MCQ (Single Correct Answer)
+2
-0.66

Let $ x $ and $ y $ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $ z = xy $ and let the mean values of $ x, y, z $ be $ \bar{x} , \bar{y} , \bar{z} $, respectively. Which one of the following statements is TRUE?

A

$ \bar{z} = \bar{x} \bar{y} $

B

$ \bar{z} \leq \bar{x} \bar{y} $

C

$ \bar{z} \geq \bar{x} \bar{y} $

D

$ \bar{z} \leq \bar{x} $

3
GATE CSE 2024 Set 1
Numerical
+2
-0

A bag contains 10 red balls and 15 blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to 3 decimal places) that both balls drawn are red is ________

Your input ____
4
GATE CSE 2023
MCQ (More than One Correct Answer)
+2
-0

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)
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