Question

In: Math

John invited four friends to his birthday party and his friends will arrive independently of one...

John invited four friends to his birthday party and his friends will arrive independently of one another. The arrival time x for each friend is uniform over (0; 4) and these arrival times are i.i.d. Answer to the following questions:

(a) the density of the arrival time who arrives at second.
(b) the probability that the second person to arrive between 0 and 2.
(c) the expected arrival time of the second person to arrive.

Solutions

Expert Solution

Let be the arrival time of 4 friends which are uniformly distributed over (0,4).

The pdf is

The cdf is

Let be the ordered statistics such that . That is is the arrival time of ith person to arrive

the pdf of is

a) The pdf for  i=2

ans: the density of the arrival time who arrives at second is

b) the probability that the second person to arrive between 0 and 2 is

ans: the probability that the second person to arrive between 0 and 2 is 0.6875

c) The expected value of is

ans: the expected arrival time of the second person to arrive is 1.6

milcah answered 6 months ago
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