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Let us suppose that some article investigated the probability of corrosion of steel reinforcement in concrete...

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Basic Math

Let us suppose that some article investigated the probability ofcorrosion of steel reinforcement in concrete structures. It isestimated that the probability of corrosion is 0.19 under specificvalues of half-cell potential and concrete resistivity. The risk ofcorrosion in five independent grids of a building with these valuesof half-cell potential and concrete resistivity. Let the randomvariable X denote number of grids with corrosion in this building.Determine the cumulative distribution function for the randomvariable X.

Round your answers to five decimal places (e.g.98.76543).

f(x)=          with x < 0

f(x)=            with 0 <= x < 1

f(x)=            with 1 <= x < 2

f(x)=            with 2 <= x < 3

f(x)=            with 3 <= x < 4

f(x)=            with 4 <= x < 5

f(x)=            with 5 <= x

Answer & Explanation Solved by verified expert
4.4 Ratings (883 Votes)

using Excel

x p cmf
0 0.348678 0.348678
1 0.408944 0.757622
2 0.19185 0.949472
3 0.045002 0.994474
4 0.005278 0.999752
5 0.000248 1
x p cmf
0 =BINOM.DIST(A2,5,0.19,0) =B2
1 =BINOM.DIST(A3,5,0.19,0) =C2+B3
2 =BINOM.DIST(A4,5,0.19,0) =C3+B4
3 =BINOM.DIST(A5,5,0.19,0) =C4+B5
4 =BINOM.DIST(A6,5,0.19,0) =C5+B6
5 =BINOM.DIST(A7,5,0.19,0) =C6+B7

f(x)=     0      with x < 0

f(x)=     0.34867844        with 0 <= x < 1

f(x)=         0.75762229    with 1 <= x < 2

f(x)=         0.949472491    with 2 <= x < 3

f(x)=     0.99447439        with 3 <= x < 4

f(x)=        0.99975239     with 4 <= x < 5

f(x)=           1 with 5 <= x

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