Question

If random variable waiting time in minutes for bus and probability density function of x is given by

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

then probability of waiting time not more than 4 minutes is equal to ______.

Options

• 0.3

• 0.8

• 0.2

• 0.5

Answer 1

If random variable waiting time in minutes for bus and probability density function of x is given by

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

then probability of waiting time not more than 4 minutes is equal to 0.8.

Explanation:

Since, f(x) = `{{:(1/5",", 0 ≤ x ≤ 4),(0",", "otherwise"):}`

So, P(0 ≤ x ≤ 4)

= `int_0^4 f(x)dx`

= `int_0^4 1/5dx`

= `1/5[x]_0^4`

= `1/5(4 - 0)`

= 0.8