Prob. distribution with pmf and need cdf?

[megr_ftw]

Homework Statement

X=demand for the magazine with pmf

x | 1 2 3 4
p(x)| .1 .2 .4 .3

Shop owner pays $1.00 for each copy of mag. and charges $2.00. If mags. left at end of week are not worth anything, is it better to order two, three, or four copies of the mag.?

I know i need to introduce the random variable Y_k = # of mags. sold, while R_k= the net profit if k mags are ordered.

So do I need to find the probability distributions for k=2,3,4,5 in order to answer the quesiton?? I am just lost on how to start this or how to get the pmf for Y

Homework Equations

binomial equation or tables?

The Attempt at a Solution

I don't know how to start this problem but for starters should I make a pmf table for the introduced random variable Y and R??

 

[lanedance]

i would use the given pmf for each separate case, bit of work but not unmanagable, then calculate the EMV for each case

so for case 1) buying a single magazine cost was $1
- each of the outcomes is 1 (if demand is 1,2,3 or 4) he will sell one magazine, so he makes $2 in all cases, EMV is $1.

for the rest of the cases you will need to incorporate the probs as the value of outcomes will vary

 

[megr_ftw]

for k=2 i got 3.8 as the profit
but for k=3 what do i change in my formula when referring to the pmf chart??

 

[lanedance]

are you sure that is profit for k=2, you need to account for the cost of buying 2 magazines

 

[lanedance]

though what you have i think is done correctly but is the revenue