Question

If X is waiting time in minutes for a bus and its p.d.f. is given by

f(x) `{:(= 1/5",", "for"  0 ≤ x ≤5","),(= 0",", "otherwise"):}`

then the probability that waiting time is between 1 and 3 is ______.

Options

• `1/5`

• `2/5`

• `3/5`

• `4/5`

Answer 1

If X is waiting time in minutes for a bus and its p.d.f. is given by

f(x) `{:(= 1/5",", "for"  0 ≤ x ≤ 5","),(= 0",", "otherwise"):}`

then the probability that waiting time is between 1 and 3 is `underlinebb(2/5)`.

Explanation:

Given p.d.f.:

f(x) `{{:(1/5",", 0 ≤ x ≤5),(0",", "otherwise"):}`

This is a uniform distribution on [0, 5].

Step 1: Find P(1 ≤ X ≤ 3)

`P(1 ≤ X ≤ 3) = int_1^3 1/5 dx`

Step 2: Integrate

= `1/5 (3 - 1)`

= `1/5 xx 2`

= `2/5`