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In: Statistics and Probability

PROBLEM 3 A fire station is located one mile from the west end of a 3...

PROBLEM 3 A fire station is located one mile from the west end of a 3 mile east-west stretch of road. (The fire station is located along that road, one mile from the west end and two miles from the east end.) Fires to which the fire truck must respond are uniformly distributed along this stretch of road. When a fire call comes, the truck leaves immediately and travels at 30 miles per hour (= 1/2 mile per minute). Let T be the time in minutes until the truck gets to the fire.

(a). Find the CDF F(t) of T, for all real numbers t.

(b). Find the density f(t) of T.

(c). Find E(T).

(d). Find var(T).

Expert Solution

The distance of the fire station from the spot of fire is uniformly distributed RV and .

Maximum time taken by the fire truck is to the east . The pdf of adds up in the interval , since the time is same to west and to east.

b)The pdf of is defined as .

For to be a pdf

The pdf of is

a) The CDF of is

c) The expected value of is

d) To find variance,

orchestra answered 2 years ago

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