Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to :

Question

Question

This question was previously asked in

NIELIT Scientific Assistant CS 5 Dec 2021 Official Paper

Answer 1

Explanation:
We are given: X ~ U[0, 4] and Y ~ U[0, 1]. Both are independent uniform distributions.

⇒ We are asked to find P(max(X, Y) > 3)

Using complement rule:

P(max(X, Y) > 3) = 1 - P(max(X, Y) ≤ 3)

Now, max(X, Y) ≤ 3 means both X ≤ 3 and Y ≤ 3

But since Y ∈ [0, 1], Y is always ≤ 3, so:

⇒ P(max(X, Y) ≤ 3) = P(X ≤ 3)

X ~ U[0, 4] ⟹ P(X ≤ 3) = (3 - 0)/(4 - 0) = 3/4

⟹ P(max(X, Y) > 3) = 1 - 3/4 = 1/4

Final Answer: Option 1) 1/4

Download Solution PDF