Question

Jepoy has one 100-peso bill, two 200-peso bills, and five 500-peso bills in his wallet. He wants to randomly pick one bill. Let X be the random variable of choosing one bill from his wallet.

Questions:

1. Construct the probability distribution table of X. [2 points]

2. Compute for the mean of X, denoted as E(X). [2 points]

3. Interpret the mean of X. [1 point]

4. Compute for the variance of X, denoted as V(X). [5 points]

5. Compute for the standard deviation of X, denoted as SD(X). [2 points]

Interpret the standard deviation of X. [1 point

Answer 1

$1:\\P\left( X=100 \right) =\frac{1}{8}=0.125\\P\left( X=200 \right) =\frac{2}{8}=0.25\\P\left( X=500 \right) =\frac{5}{8}=0.625\\\begin{matrix} x& 100& 200& 500\\ P\left( X=x \right)& 0.125& 0.25& 0.625\\\end{matrix}\\2:\\EX=100\cdot 0.125+200\cdot 0.25+500\cdot 0.625=375\\3:\\At\,\,average\,\,375-peso\,\,bill\,\,is\,\,taken\\4:\\EX^2=100^2\cdot 0.125+200^2\cdot 0.25+500^2\cdot 0.625=167500\\V\left( X \right) =EX^2-\left( EX \right) ^2=167500-375^2=26875\\5:\\SD\left( X \right) =\sqrt{V\left( X \right)}=\sqrt{26875}=163.936\\6:\\At\,\,average\,\,the\,\,range\,\,of\,\,bill\,\,amount\,\,is\,\,\pm 164 peso$