GUJCET 2018 Math Solved Paper

Given, f(x)=3x+2
applying expectation on both sides, we get
E(f(x))=3E(x)+2 (by the properties of expectation)
mean E(x)=

n

∑

i=1

xiP(xi)
Given, number of samples n=4
Hence, mean =

4

∑

i=1

xiP(xi)
substituting the values from the table we get,
=1(‌

1

6

)+2(‌

1

3

)+3(‌

1

3

)+4(‌

1

6

)
=‌

1+4+6+4

6

=‌

15

6

‌‌E(x)=‌

5

2

Therefore, E(f(x))=3(‌

5

2

)+2
=‌

19

2