Question

Let $X$ be a discrete random variable whose spectrum consists of $x_{i}=(-1)^{i+1}\frac{3^{i}}{i},$ $i=1,2,...$ and $f_{i}=P(X=x_{i})=\frac{2}{3^{i}},$ $i=1,2,...$ Show that $E(X)$ does not exist.​

Answer 1

Answer:

Let XX be a discrete random variable whose spectrum consists of x_{i}=(-1)^{i+1}\frac{3^{i}}{i},xi=(−1)i+1i3i, i=1,2,...i=1,2,... and f_{i}=P(X=x_{i})=\frac{2}{3^{i}},fi=P(X=xi)=3i2, i=1,2,...i=1,2,... Show that E(X)E(X) does not exist.

Step-by-step explanation:

Let XX be a discrete random variable whose spectrum consists of x_{i}=(-1)^{i+1}\frac{3^{i}}{i},xi=(−1)i+1i3i, i=1,2,...i=1,2,... and f_{i}=P(X=x_{i})=\frac{2}{3^{i}},fi=P(X=xi)=3i2, i=1,2,...i=1,2,... Show that E(X)E(X) does not exist.

Answer 2

Answer:

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