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