Question

If the cumulative distribution function of X is given by the function below, then what is P (X < 0.80).
f(x) = 0 , if x ≤ 0
f(x) = x^2, if 0 < x ≤ 1
f(x) = 1 , if x > 1

Answer 1

Answer on Question #43225-Math-Statistics and Probability

If the cumulative distribution function of $X$ is given by the function below, then what is $P(X < 0.80)$.

$$f(x) = 0, \text{ if } x \leq 0$$ $$f(x) = x^2, \text{ if } 0 < x \leq 1$$ $$f(x) = 1, \text{ if } x > 1$$

Solution

The cumulative distribution function (CDF) of a random variable $X$ is denoted by $f(x)$, and is defined as $f(x) = \Pr(X \leq x)$. So

$$P(X < 0.80) = f(0.80) = 0.80^2 = 0.64.$$

Answer: 0.64.

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