Write out the formula for combinations. Explain each variable. Write out the for

Question

Write out the formula for combinations. Explain each variable. Write out the formula for permutations. Explain each variable. Which one is usually larger? Why? If your success as a stock trader for picking profitable trades is 50% and you make a total of 8 trades, what are the chances that, 3 or more, of the 8 trades will be profitable? What are the chances that none are profitable? What's the median of this set of numbers: 7, 8, 9, 15, 16, 19, 15, 25 What's the variance of this series: 15, 18, 44, 32, 19, 21, 27, 20, 23

Explanation / Answer

6) The formula for no. of combinations is written as nCr. This represents the number of all combinations of n things taken r at a time. The formula to calculate the combinations is:

nCr = n! / (r!)(n-r)!

7) The formula for the no. of permuations is written as nPr. This represents the number of permuations of n things taken r at a time. The formula to calculate the permuations is:

nPr = n! / (n - r)!

8) The permuations are usually larger than the combinations. This is beacuse in combinations, order does not matter, whereas in permuations order matters and is significant.

9) P(Success chance of a trader) = 0.5

Total trades = 8

Chances that 3 or more of the 8 trades will be profitable is

1 - P(only one trade profitable) - P(only 2 trades profitable)

P(only one trade profitable) = (0.5)^1 * (0.5)^7 = 0.00390625

P(only 2 trades profitable) = (0.5)^2 * (0.5)^6 = 0.00390625

So Chances that 3 or more of the 8 trades will be profitable = 1 - 0.00390625 - 0.00390625

= 0.9921875

10) For finding median we can use the median() function in R

data <- c(7,8,9,15,16,19,15,25)
median(data)

= 15

11) For finding variance, we can use the var() function in R

data <- c(15,18,44,32,19,21,27,20,23)
var(data)

=80

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