Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=0.1. What isthe conditional probability that a repair takes at least 10 hours, given that it takes more than 8 hours?

Step-by-step explanation:

Given that the time  (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=0.1.

Let X be the time taken for a repair

The conditional probability that a repair takes at least 10 hours, given that it takes more than 8 hours

= P(X≥10/x>8)

=

Parameter = 0.1

F(10) =

F(8) =

Hence answer  =0.8187

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: