# A Couple of Probability & Statistics Questions

1. Jan 13, 2009

### havinnoj

1. The problem statement, all variables and given/known data
I have a table with a data set #, and 2 variables (W and P) with values in the table.

2. Relevant 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)

3. The attempt at a solution

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

2. Jan 13, 2009

### 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?

3. Jan 13, 2009

### kenewbie

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

4. Jan 13, 2009

### havinnoj

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

Anybody have an idea about the first one?

5. Jan 13, 2009

### danago

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.

$$\sum _{i=1} ^{n} W_i P_i = W_1P_1+W_2P_2+...+W_nP_n$$
$$\sum _{i=1} ^{n} P_i = P_1+P_2+...+P_n$$