You are a contestant on a TV game show, there are four identical-looking suitcases containing $200, $400, $800, and $1,600. You start the game by randomly choosing a suitcase. Among the three unchosen suitcases, the game show host opens the suitcase that holds the least money. The host then asks you if you want to keep your suitcase or switch one of the other remaining suitcases. For the following analysis, use the following notation for events: A) C is the even that you choose a suitcase with i dollars.
B) O; denotes the event that the host opens a suitcase with i dollars.
C) R is the reward in dollars that you keep.
1) You refuse the host's offer and open the suitcase you first chose. Find the Probability Mass Function (PMF) of R and the expected value E[R].
2) You switch and randomly choose one of the two remaining suitcases. You receive the R dollars in this chosen suitcase. Find the Probability Mass Function (PMF) and expected value of R.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

idk man good luck man

i think the correct option is the second option.

27 +27 or 27times 2=54

the diffrence is 0