A Couple of Probability & Statistics Questions

[havinnoj]

Homework Statement

I have a table with a data set #, and 2 variables (W and P) with values in the table.

Homework Equations

The equation (which I don't know what it means) says V= (summation with n on top and i=1 below Wi X Pi)/(summation with n on top and i=1 on bottom X Pi)

The Attempt at a Solution

What are the summations meaning and what do the subscript "i"'s mean?

 

[havinnoj]

Questions 2 is "You are reviewing a business decision where you have calculated the profit for 5 possible business scenarios. If the probabilities of occurrence for four of the scenarios are 12%, 10%, 21%, and 30% respectively; what is the percent probability of occurence for the fifth scenario.

Does this question even make sense?

 

[kenewbie]

Questions 2 is "You are reviewing a business decision where you have calculated the profit for 5 possible business scenarios. If the probabilities of occurrence for four of the scenarios are 12%, 10%, 21%, and 30% respectively; what is the percent probability of occurence for the fifth scenario.
Does this question even make sense?

I read that as "there are exactly 5 possible scenarios". In a valid probability-model, what do you know about the sum of all possible probabilities?

k

 

[havinnoj]

I read that as "there are exactly 5 possible scenarios". In a valid probability-model, what do you know about the sum of all possible probabilities?

k

27%. I love when they are easier than you think! Thank you!

Anybody have an idea about the first one?

 

[danago]

Homework Statement

I have a table with a data set #, and 2 variables (W and P) with values in the table.

Homework Equations

The equation (which I don't know what it means) says V= (summation with n on top and i=1 below Wi X Pi)/(summation with n on top and i=1 on bottom X Pi)

The Attempt at a Solution

What are the summations meaning and what do the subscript "i"'s mean?

What is X? Should that just be Pi?

Anyway, the top summation means that you are starting from the "i=1" data point (i.e. the first W and P), multiplying W and P, then doing the same for the second data points (i=2) all the way up to the n'th W and P, and then adding them all up.

In general,

$$\sum _{i=a} ^{n} f(i) = f(a) + f(a+1) + f(a+2) + ... + f(n)$$

So it just means that you start with i=a, and plug it into the function f(i). Then continuously increase 'i' by integer steps until you get to i=n, each time plugging it into the function f(i). Then simply add each f(i) that you calculated along the way.

So in your cases:

$$\sum _{i=1} ^{n} W_i P_i = W_1P_1+W_2P_2+...+W_nP_n$$

$$\sum _{i=1} ^{n} P_i = P_1+P_2+...+P_n$$

 

[havinnoj]

Awesome! Thank you!