Question

You have a bag containing 3 red, 5 blue, 10 green, and 2 yellow marbles. You reach in select a marble and win $10 for a red, $20 for a blue, $50 for a green, and $2 for a yellow. 1. Make a discrete probability distribution table. X | P(x) 2. Find the mean (expected value) for this "game". Extend the table from #1 using the correct formula for column 3 P(x) 3. Find the standard deviation for this "game". Extend the table from #2 using the correct formula for column 4 P(x)

Answer 1

Let X be the Tandom variabl reprekenhing winning maney. So, the values X can be Soln 2, 10, 20 4 50 1-e 2, 10, 20, 50 centains 3 red, S blue, l0green Nouo, the and 2 yello mas bles Tolal bales 3t St 10+2 2 20 PCting a yellow ball P(wins 2) PCx=2) 2 20 3 red ball) P(winsfio)PCgelhing a P(wins fa) - P(9etinga P(wind ts) P(geting a gen balt) prebahilily dis hibuhion table (2) P(xe 10) 20 a blue ball) Pix- 20) PCX So) 20 20 Discrele 0.2 l C lo 15 20 20 2o 5.0 20 4 4 5 0 25 0 50 MX-pm) 31.7 E() Expected value Map(n)-317 (3) O.2 1 So 10 1-5 20 100 20 5.0 4 12 SO.0 5 0 21-0 1 Saipta) 364 Expx31-7 Vaniamce, 31-7) =1365Y-1004.89 E()ET) 360 ) V(x) 18.907/ AS Standard duhonJv() 360 Nr A