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
Algebra.Com
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.
 = \frac{t_1 - t_0}{t - 0})
 = \frac{t_1 - t_0}{t})
There's not much more I can say since we don't know the values of , , and
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Part (b)
Let 
which represents the probability T is between and . We found this back in part (a)
Then we can say that
 = 1 - P(T \le t_0))
 = 1 - \frac{t_0}{t})
 = \frac{t}{t} - \frac{t_0}{t})
 = \frac{t-t_0}{t})
We'll assign this to the variable B.
So,
 = \frac{A}{B})
 = A \div B)
 = \frac{t_1 - t_0}{t} \div \frac{t-t_0}{t})
 = \frac{t_1 - t_0}{t} \times \frac{t}{t-t_0})
 = \frac{(t_1 - t_0)*t}{t*(t-t_0)})
 = \frac{t_1 - t_0}{t-t_0})
I'm using the idea of conditional probability
P(A given B) = P(A and B)/P(B)
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