Question

The time T before a certain bereset is exponentially distributed with the mean of 3 hours.

a) whit is the probability that 5 hours pass before the circuit breaker turnsn off for the first time?

b) SUppose a random vairable V is given by V = 3y + 1. Find the density function of V

Answer 1

Let time before a certain bereset be 'X'

Where E(X) = ...............Therefore

=

a) whit is the probability that 5 hours pass before the circuit breaker turns off for the first time?

If 5 hours are passing before turning off, that means it will definitely take more than 5 hours t to turn off

P(X > 5) = 1 - P(X <5)

=

b) SUppose a random vairable V is given by V = 3y + 1. Find the density function of V

Now assume that instead of variable X it is Y

We begin by the taking the cdf of V and then working towards cdf of Y.

P(V < v) = P( 3Y + 1 < v)

= P(3Y < v - 1)

=

= ....................using cdf of Y

=

=

If we differentiate it w.r.t 'v' we get

...........We differentiate because for getting pdf to cdf we integrate the function.