There are total 5 batches and two boards are selected from each batch for inspection.
Let the boards are numbered from 1 to 5.
If the selected boards are 1 and 2, then it is represented in pair as (1, 2).
If the selected boards are 1 and 3, then it is represented in pair as (1, 3).
Similarly, other pairs can be obtained.
a) Let X be the number of defective boards observed among the two inspected.
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."
b)
"\\begin{matrix}\n x & 0 & 1 & 2 \\\\\n p(x) & 0.3 & 0.6 & 0.1 \n\\end{matrix}""\\mu_X=\\displaystyle\\sum_{i=1}^nx_ip(x_i)"
"\\mu_X=0\\cdot0.3+1\\cdot0.6+2\\cdot 0.1=0.8"
"Var(X)=\\sigma_X^2=\\displaystyle\\sum_{i=1}^n(x_i-\\mu_X)^2p(x_i)""\\sigma_X^2=(0-0.8)^2\\cdot0.3+(1-0.8)^2\\cdot0.6+(2-0.8)^2\\cdot0.1=0.36""\\sigma_X=\\sqrt{\\sigma_X^2}=\\sqrt{0.36}=0.6"
"\\mu_X=0.8, \\ \\sigma_X=0.6"
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