Cumulative Distribution Function exercise

Hello to everyone! I need help with the following exercise:

“Let X=1/2N², where N is an integer random variable with value in -1≤N≤3. Calculate the CDF (Cumulative Distribution Function) of X and use it to calculate the probability of the following events: {X≤0}{2<X≤3}{X<2} and {X≥2}.”
The results are: 1/5, 0, 3/5 and 2/5.

I know how to calculate the probability of the events, but I don't know how to calculate the CDF of X.

Please, can you help me?

Kalynda said:

Hello to everyone! I need help with the following exercise:

“Let X=1/2N², where N is an integer random variable with value in -1≤N≤3. Calculate the CDF (Cumulative Distribution Function) of X and use it to calculate the probability of the following events: {X≤0}{2<X≤3}{X<2} and {X≥2}.”
The results are: 1/5, 0, 3/5 and 2/5.

I know how to calculate the probability of the events, but I don't know how to calculate the CDF of X.

Please, can you help me?

Click to expand...

Since I agree with your answers for P(X), I assume you will recognize this table:

\(\displaystyle \begin{matrix}N & X \\ -1 & 1/2 \\0 & 0 \\ 1 & 1/2 \\ 2 & 2 \\ 3 & 4\ 1/2 \end{matrix} \)

Each allowed value for N, and thus each line of the table, has a probability of 1/5.

Now rearrange the Table in order by X, combining the two equal values of X. To make the CDF of X, write down the running sum of P(X).

\(\displaystyle \begin{matrix}X & P(X) & \Sigma P(X) \\ 0 & 0.2 & 0.2 \\1/2 & 0.4 & 0.6 \\ 2 & 0.2 & 0.8 \\4.5 & 0.2 & 1\end{matrix} \)

thanks a lot