Customers arrive randomly at a bank tellers window Given tha

Customers arrive randomly at a bank teller\'s window. Given that one customer arrived during a particular 10-minute peroid, 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(X8)

c) P(2X8)

d) E(X)

e) Var(X)

Solution

a)

As the length of the distirbution is 10-0 = 10, then,

f(x) = 1/10 , 0<x<10
0 , otherwise

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b)

P(x>=8) = (10-8)/(10-0) = 0.2 [ANSWER]

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c)

P(2<=x<=8) = (8-2)/(10-0) = 0.6 [ANSWER]

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d)

E(x) = (a+b)/2 = (0+10)/2 = 5 [answer]

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e)

Var(x) = (b-a)^2/12 = (10-0)^2/12 = 8.333333333 [ANSWER]