Question

Assume that X is a random variable describing the outcomes of a radar gun used by a police officer to catch drivers exceeding the speed limit. The radar gun does not record the true speed of the car. It either records the speed of the driver as 5 miles per hour (mph) too fast or 5 mph too slow. Suppose the police officer takes a sample equal to 1. The probability distribution for a sample equal to 1 is as follow.

Xi =

Xi	P(Xi)
?+5	0.5
?-5	0.5

a) Find the expected value of the speed radar

b) fIND THE VARIANCE OF THE RANDOM VARIABLE

c) Will the radar gun ever record the correct speed? why, why not?

Answer 1

a)

E(X) =

= ( + 5) * 0.5 + ( - 5) * 0.5

= 0.5 + 2.5 + 0.5 - 2.5

=

b)

E(X²) =

= ( + 5)² * 0.5 + ( - 5)² * 0.5

= ( + 25 + 10) * 0.5 +  ( + 25 - 10) * 0.5

= 0.5 + 12.5 + 5 +  0.5 + 12.5 - 5

= + 25

Var(X) = E(X²) - E(X)²

= + 25 -

= 25

c)

The radar gun would record the correct speed when the speed is + 5 or - 5. At that time the radar  records the speed of the driver as 5 miles per hour (mph) too fast or 5 mph too slow.