Answer to Question #154826 in Statistics and Probability for NIDHI JOSHI

Question

For the given probability distribution function

X=x 1. 2 3. 4. 5

P[X=x] 0.1 0.3 0.2 0.2 0.2

E(x) =?

E(2x+5) =?

E(x/2+3)=?

E(x ² )

Answer 1

Find E(X):

solution :

we need to multiply the corresponding X outcomes with the corresponding probabilities, in order to compute the population mean μ.

Therefore, the population mean is calculated as follows:

$μ ​ = ​ ∑ ​ X *p(X i ​ )$

=1⋅0.1+2⋅0.3+3⋅0.2+4⋅0.2+5⋅0.2

=3.1

Hence E(X)= 3.1

Find E(2x+5):

Solution :

We know E[aX + b] = aE[X] + b

Hence E(2X+5)= 2E(X)+5

=2(3.1)+5

=11.2

find E(X/2+3)= $\frac{1}{2}E(X)+3$

=$\frac{1}{2}(3.1)+3$

=4.55

find $E(X^2):$

solution:

we need to multiply the corresponding squares $X^2$ of the outcomes with the corresponding probabilities, in order to compute $E(X^2)$ :

$E(X ^ 2 ) ​ = ∑ X ^ 2 ​* p(X ​)$

=$1 ^ 2 ⋅0.1+2 ^ 2 ⋅0.3+3 ^ 2 ⋅0.2+4 ^ 2 ⋅0.2+5 ^ 2 ⋅0.2= 11.3$

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