Suppose the cumulative distribution function of a random variable X is given by :Calculate P(1 < X < 3)?

To calculate $P(1 < X < 3)$ using the cumulative distribution function (CDF), follow these steps:

1. Break Down the Problem

We need to find the probability that the random variable $X$ falls between 1 and 3. This can be expressed using the cumulative distribution function $F(x)$.

2. Relevant Concepts

The cumulative distribution function $F(x)$ gives the probability that a random variable $X$ is less than or equal to $x$: $P(a < X < b) = F(b) - F(a)$ Thus, $P(1 < X < 3) = F(3) - F(1)$

3. Analysis and Detail

1. Compute $F(3)$ - Find the value of the CDF at $x = 3$.
2. Compute $F(1)$ - Find the value of the CDF at $x = 1$.
3. Calculate the Probability - Subtract $F(1)$ from $F(3)$.

4. Verify and Summarize

Ensure that you have the correct values for $F(3)$ and $F(1)$ and perform the subtraction accurately.

Final Answer

The final result will be: $P(1 < X < 3) = F(3) - F(1)$

To provide a numeric answer, values for $F(3)$ and $F(1)$ must be given or specified.