1
GATE ME 2024
Numerical
+2
-1.33

Let $X$ be a continuous random variable defined on $[0, 1]$ such that its probability density function $f(x) = 1$ for $0 \leq x \leq 1$ and $0$ otherwise. Let $Y = \log_e (X + 1)$. Then the expected value of $Y$ is _____ . (rounded off to 2 decimal places)

Your input ____
2
GATE ME 2016 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Three cards were drawn from a pack of $$52$$ cards. The probability that they are a king, a queen, and a jack is
A
$${{16} \over {5525}}$$
B
$${{64} \over {2197}}$$
C
$${3 \over {13}}$$
D
$${8 \over {16575}}$$
3
GATE ME 2016 Set 2
Numerical
+2
-0
The probability that a screw manufactured by a company is defective is $$0.1$$. The company sells screws in packets containing $$5$$ screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is _________.
Your input ____
4
GATE ME 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event that a tail occurs on the third toss. Let $$Z$$ be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?
A
$$X$$ and $$Y$$ are not independent
B
$$Y$$ and $$Z$$ are dependent
C
$$Y$$ and $$Z$$ are independent
D
$$X$$ and $$Z$$ are independent
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