GATE 2023 ST – Question 15

Probability · Random Variables and Transforms · 1 mark · Multiple choice

Let Φ be the standard normal CDF. X has CDF F(x)=Φ(x) for x<−1 and Φ(x+1) for x≥−1. Which holds?

Show answer and explanation

Correct answer: (A) P(X≤−1)=1/2

Explanation

By right-continuity P(X≤−1)=F(−1)=Φ(0)=1/2. The atom is F(−1)−F(−1−)=1/2−Φ(−1),not 1/2; the strict probability is Φ(−1),and F(0)=Φ(1). **A**.

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