SOLUTION: A telephone call occurs at random in the interval (0, t). Let T be its time of occurrence. Determine, where 0 <= t0 <= t1 <= t (a) P(t0 <= T <= t1) (b) P(t0 <= T <= t1

Click here to see ALL problems on Probability-and-statistics

Question 1183249: A telephone call occurs at random in the interval (0, t). Let T be its time of
occurrence. Determine, where 0 <= t0 <= t1 <= t
(a) P(t0 <= T <= t1)
(b) P(t0 <= T <= t1 | T >= t0)

Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

Part (a)

I'm assuming we're dealing with a uniform distribution.

There's not much more I can say since we don't know the values of , , and

========================================================================
Part (b)

Let which represents the probability T is between and . We found this back in part (a)

Then we can say that

We'll assign this to the variable B.

So,

I'm using the idea of conditional probability
P(A given B) = P(A and B)/P(B)

SOLUTION: A telephone call occurs at random in the interval (0, t). Let T be its time of occurrence. Determine, where 0 <= t0 <= t1 <= t (a) P(t0 <= T <= t1) (b) P(t0 <= T <= t1 | T >= t0