Question

Let $X$ be a random variable having $U(0,10)$ distribution and $Y = X - [X]$, where $[X]$ denotes the greatest integer less than or equal to $X$. Then $P(Y > 0.25)$ equals ..............

Hint:

The fractional part of a continuous uniform variable over integers is uniformly distributed on (0,1).

Answer 1

Correct Answer: 0.75

Step 1: Understand fractional part distribution.
For $X \sim U(0,10)$, the fractional part $Y = X - [X]$ is uniformly distributed over $(0,1)$.

Step 2: Compute the required probability.
\[ P(Y > 0.25) = 1 - P(Y \le 0.25) = 1 - 0.25 = 0.75. \]

Final Answer: \[ \boxed{P(Y > 0.25) = 0.75.} \]