Question

Problem 2. Let us suppose that some article investigated the probability of corrosion of steel reinforcement in concrete structures. It is estimated that the probability of corrosion is 0.1 under specific values of half-cell potential and concrete resistivity. The risk of corrosion in five independent grids of a building with these values of half-cell potential and concrete resistivity is investigated now. Let the random variable X denote number of grids with corrosion in this building. Determine the probability mass function of X.

Answer 1

Ans:

Let X be the number of grids with corrosion in this building.

Then X has binomial distribution with n=5 and p=0.1

P(x=k)=⁵C_k*0.1^k*(1-0.1)^5-k

Using above formula,develop the pmf for X:

e.g. P(x=0)=⁵C₀*0.1^0*(1-0.1)^5=0.5905

x	P(x)
0	0.5905
1	0.3281
2	0.0729
3	0.0081
4	0.0005
5	0.0000