Question

Correct answer please

Answer 1

50.75

Explanation:

We have:

`E[g(x)] = \int\limits^(\infty)_(-\infty) {g(x)f(x)} \, dx \\\\= \int\limits^(1)_(-\infty) {g(x)(0)} \, dx+\int\limits^(6)_(1) {g(x)(2)/(x) } \, dx+\int\limits^(\infty)_(6) {g(x)(0)} \, dx\\\\= \int\limits^(6)_(1) {g(x)(2)/(x) } \, dx\\\\=\int\limits^(6)_(1) {(4x+3)(2)/(x) } \, dx\\\\=\int\limits^(6)_(1) {(4x)(2)/(x) } \, dx + \int\limits^(6)_(1) {(3)(2)/(x) } \, dx\\\\=\int\limits^(6)_(1) {8} \, dx + \int\limits^(6)_(1) {(6)/(x) } \, dx\\\\`

`=8\int\limits^(6)_(1) \, dx + 6\int\limits^(6)_(1) {(1)/(x) } \, dx\\\\= 8[x]^(^6)_(_1) + 6 [ln(x)]^(^6)_(_1)\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74`