# Distribution with pmf and rand. variables.

• megr_ftw
In summary, the conversation discusses the demand for a magazine with a given probability mass function and the profit for a shop owner who buys and sells the magazine. The question is whether it is better to order two, three, or four copies of the magazine. The conversation also introduces the random variables Y_k and R_k, and discusses the possibility of finding the expected value for the number of magazines sold. The conversation suggests creating a table to calculate the profit for all combinations of magazines bought and sold, and using this information to determine the optimal number of magazines to order.
megr_ftw
I posted this in the wrong section before and meant to put it here, so i apologize if you seen this before.

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 variables:
Y_k = # of mags. sold
R_k= the net profit if k mags are ordered.

I am NOT trying to just get the answer out of someone, I just need advice on how to start this..
Do I need to make another pmf for Y_k and R_k? Or do I need to figure out expected value.
just a hint may help me understand this problem

It looks like an open-ended question. First step could be to write down the profit for all 16 combinations {(1 bought, 1 sold), (1 bought, 2 sold), ...} perhaps as a 4x4 table.

i don't think its open ended, because R_k= -1k+2*Y_k since R_k is the profit
could i simply find the expected value is 1, 2, or 3 are sold that's it?

That's the open-ended part, it's up to you to choose a selection criteria. Expected value is only one of infinitely many possibilities. It's good that you've got a formula for the profit though it's important to actually look at the values and their relative probabilities (for example, with an appropriate chart) otherwise important details can be hidden.

Last edited:
okay the profit for k=2 i got 3.8

when i am calculating it for when k=3 is this equation correct? -1(3)+2(.1*1+.2*3.8+.4*3.8+.3*3.8)
i may be going off a longshot but i used the profit from k=2 for the values of x in this equation.

I just want to make sure I am doing k=3 right so i can figure out when k=4...

## 1. What is the difference between pmf and rand. variables?

The pmf (probability mass function) is a function that maps each possible value of a discrete random variable to its corresponding probability. A random variable, on the other hand, is a variable whose value is determined by the outcome of a random process. In other words, a pmf describes the probability distribution of a random variable.

## 2. How do you calculate the expected value of a distribution with pmf and rand. variables?

The expected value of a random variable is the sum of each possible value multiplied by its corresponding probability. In other words, it is the weighted average of all possible outcomes. To calculate the expected value, you would need to multiply each possible value by its probability and then sum them all together.

## 3. Can a pmf have negative probabilities?

No, a pmf cannot have negative probabilities. The probabilities in a pmf must be non-negative and sum up to 1. This is because probabilities represent the likelihood of an event occurring, and it cannot have a negative likelihood.

## 4. How do you use pmf and rand. variables in real-life scenarios?

Pmf and rand. variables are commonly used in statistics and probability to model and analyze random processes. They can be used to make predictions and decisions based on uncertain outcomes, such as in finance, marketing, and engineering. For example, a company may use pmf and rand. variables to model the probability of a product being successful in the market.

## 5. What other types of distributions are commonly used besides pmf and rand. variables?

Some other commonly used distributions include continuous distributions, such as the normal distribution, which is used to model continuous random variables. There are also multivariate distributions, which involve multiple random variables, and joint distributions, which describe the probability of multiple events occurring simultaneously.

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