Customers arrive randomly at a bank tellers windowGiven that

Customers arrive randomly at a bank teller’s window.Given that one customer arrived during a particular 10-minute period, let X equal the time within the 10 minutes that the customer arrived. If X is U(0, 10), find

(a) The pdf of X.
(b) P(X 8).
(c) P(2 X < 8).
(d) E(X).
(e) Var(X).

Solution

a) pdf of X = 1/10 when x belongs to ( 0,10)......
   = 0 otherwise

b) P [ X >=8] = INTEGRATION FROM 8 TO 10 [ dx/10 ] = 1/5...
c) P [ 2 <= X < 8 ] = INTEGRATION FROM 2 TO 8 [ dx /10 ] = 3/5...

d) E(X) = (0+10)/2 =5..
e) var(X) = ( 10 - 0) ^2 /12 = 100 /12 = 25/3 =8.333..