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June 10th, 2015, 03:59 PM   #1
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Math Focus: Statistics
Expected Total value

Could anyone check my working out

Two coins are selected at random from a wallet containing four 5 cent pieces, one 10 cent piece, three 20 cent pieces and two 50 cent pieces.
What is the expected total value of the two coins?

expected value = mean = ∑(x).P(x)

But before using the formula you should created your Probability distribution table:

cents...........5c.....10c....20c.....50c
value of x......4......1.......3........2
P(x=x)..........2/5...1/10...3/10...1/5

Probability Distribution( from the table above)

X........... 1.... 2..... 3..... 4
P(X=x)...0.1.. 0.2... 0.3... 0.4

By using the formula(∑(x).P(x)) all x values were multiplied by its probability and then add them together. = 3

I dont know if I do the right thing because and if I do some mistakes I would like to learn from it.
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June 11th, 2015, 07:46 AM   #2
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\begin{matrix}
Outcome\ x_i & 10¢ & 15¢ & 25¢ & 30¢ & 40¢ & 55¢ & 60¢ & 70¢ & $1 \\
Probability\ p_i & \frac{\binom{4}{2}}{\binom{10}{2}} & \frac{4\cdot 1}{\binom{10}{2}} & \frac{4\cdot 3}{\binom{10}{2}} & \frac{1\cdot 3}{\binom{10}{2}} & \frac{\binom{3}{2}}{\binom{10}{2}} & \frac{4\cdot 2}{\binom{10}{2}} & \frac{1\cdot 2}{\binom{10}{2}} & \frac{3\cdot 2}{\binom{10}{2}} & \frac{\binom{2}{2}}{\binom{10}{2}}
\end{matrix}
$\displaystyle E[X]=\sum_{i=1}^9 x_i\cdot p_i=0.38$
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