Let the boards are numbered from 1 to 5.
a) Let X be the number of defective boards observed among the two inspected.
"(1,2), (1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)"
If the boards 1 and 2 are the only defective boards in a lot of five, then
"(1,2),x=2;(1,3),x=1;(1,4),x=1;(1,5),x=1;"
"(2,3),x=1;(2,4),x=1;(2,5),x=1;"
"(3,4),x=0;(3,5),x=0;(4,5),x=0."
"\\begin{matrix}\n x & 0 & 1 & 2 \\\\\n p(x) & 0.3 & 0.6 & 0.1\n\\end{matrix}"
b)
"\\sigma_X^2=(0-0.8)^2\\cdot0.3+(1-0.8)^2\\cdot0.6+(2-0.8)^2\\cdot0.1""\\sigma_X^2=0.36"
"\\sigma_X=\\sqrt{\\sigma_X^2}""\\sigma_X=\\sqrt{0.36}=0.6"
"\\mu_X=0.8,\\ \\sigma_X=0.6"
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