Question

(a) If the probability density of X is given by

f(x)=
1 / x(In 3)
0

for 1 elsewhere
​
find E(X),E(X²) , and E(X³) ). (b) Use the results of part
(a) to determine E(X³+2X²− 3X+1)

Answer 1

To find E(X), E(X²), and E(X³) for the given probability density function, we need to calculate the definite integrals of X, X², and X³ multiplied by the probability density function.

Step-by-step explanation:

To find E(X), E(X²), and E(X³) for the given probability density function f(x) = 1 / (x ln 3) for 1 < x <= 3, and 0 elsewhere, we need to calculate the definite integrals of X, X², and X³ multiplied by f(x).

1. E(X) = ∫ (x * f(x)) dx from 1 to 3

2. E(X²) = ∫ (x² * f(x)) dx from 1 to 3

3. E(X³) = ∫ (x³ * f(x)) dx from 1 to 3

By evaluating these definite integrals, we can find the expected values of X, X², and X³.