Verify that the following function is a cumulative distribution function. f(x) =
0 x < 1
0.5 1 < x < 3
1 3 < x
Round your answers to 1 decimal place (e. g. 98.7). Determine:
1) P(x < 3) =
2) P(x < 2) =
3) P(1 < x < 2) =
4) P(x > 2) =

The probabilities are:

Given function is:

Verification that f(x) is Cumulative distribution function:

1. Since for x > 3, f(x)  = 1, thus we have

2. Since for x < 1, f(x) = 0, thus we have

3. Since values of f(x) are not decreasing as x is increasing, thus f(x) is non decreasing.

4. f(x) is right continuous too.

Thus f(x) is a cumulative distribution function.

The Probabilities are calculated as follows:

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Following are the answer to this question:

Step-by-step explanation:

In the given equation there is mistyping so, correct equation and its calculation can be defined as follows:

Given:

Calculated value:

That's why the given equation is true.

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step-by-step explanation:

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