# Prob. distribution with pmf and need cdf?

• megr_ftw
In summary, the conversation discusses the demand for a magazine with a given probability distribution and the decision of how many copies to order based on the cost and potential profit. The random variables Y and R are introduced and the question asks for the probability distributions for different values of k. The suggested approach involves creating separate pmf tables for each case and calculating the expected monetary value (EMV) for each. The conversation then discusses the calculation for k=2 and asks for clarification on how to incorporate the pmf chart for k=3.
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??

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

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

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

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

## 1. What is a probability distribution with PMF?

A probability distribution with PMF (Probability Mass Function) is a mathematical function that describes the probability of a discrete random variable taking on each possible value. It shows the likelihood of each outcome occurring.

## 2. How is PMF different from PDF?

PMF is used for discrete random variables, while PDF (Probability Density Function) is used for continuous random variables. PMF gives the probability of a specific value occurring, while PDF gives the probability of a range of values occurring.

## 3. What is the formula for PMF?

The formula for PMF is P(X=x) = f(x), where P is the probability, X is the random variable, and f(x) is the PMF function.

## 4. Can you give an example of a PMF?

Yes, for example, if we roll a fair six-sided die, the PMF would be P(X=1) = 1/6, P(X=2) = 1/6, P(X=3) = 1/6, P(X=4) = 1/6, P(X=5) = 1/6, and P(X=6) = 1/6. This shows that each outcome has an equal probability of occurring.

## 5. Why do we need the CDF in addition to the PMF?

The CDF (Cumulative Distribution Function) gives the probability that a random variable is less than or equal to a certain value. It provides a more complete picture of the probability distribution and can be used to calculate probabilities for a range of values. It is also useful for finding percentiles and measuring the spread of the distribution.

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