1. ## random variable

Suppose that an ant is walking along a straight tunnel. Let P(t)∈R denote his position along the tunnel. Suppose that his velocity is 15 mm/s and that his initial position P(0)=Po is a random variable that is uniform in [0.30]

Sketch two sample paths P(t) for t=0 to t=3s.

2. Originally Posted by winganger
Suppose that an ant is walking along a straight tunnel. Let P(t)∈R denote his position along the tunnel. Suppose that his velocity is 15 mm/s and that his initial position P(0)=Po is a random variable that is uniform in [0.30]

Sketch two sample paths P(t) for t=0 to t=3s.
Initial position may start anywhere between zero and thirty with equal probability. After that, velocity is constant, so after three seconds, the ant has moved 45 millimeters.

The ant will finish at either 45 or 75 millimeters.

3. one more question:
what is the probability that the ant reach 45, and 70millimeters? is it a constant probabilty from 30 to 70?

4. Originally Posted by winganger
one more question:
what is the probability that the ant reach 45, and 70millimeters? is it a constant probabilty from 30 to 70?
The probability the ant reaches 45 is the same as 75 and any number in between, so, yes, there is a constant probability because the distribution is uniform.

5. Originally Posted by colby2152
The probability the ant reaches 45 is the same as 75 and any number in between, so, yes, there is a constant probability because the distribution is uniform.
can you tell me the value of that probability?