The number of pits in a corroded steel coupon follows a Poisson distribution with a mean of

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The number of pits in a corroded steel coupon follows a Poisson distribution with a mean of 6 pits per \(\mathrm{cm}^{2}\). Let \(X\) represent the number of pits in a \(1 \mathrm{~cm}^{2}\) area. Find

a. \(P(X=8)\)

b. \(P(X=2)\)

c. \(P(X<3)\)

d. \(P(X>1)\)

e. \(\mu_{X}\)

f. \(\sigma_{X}\)

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