Chapter 5: Q.5.10 (page 346)

$f (x)$ for a continuous probability function is $1 5$ , and the function is restricted to $0 \leq x \leq 5$ . What is $P (x < 0)$ ?

Short Answer

Expert verified

The value of the $P (x < 0)$ iszero.

Step by step solution

Given information

$f (x)$ for a continuous probability function is $1 5$

The function is restricted to $0 \leq x \leq 5$

Solution

Here, the probability density function of the continuous random variable $X$ is defined as:

$f (x) = \{\begin{cases} \frac{1}{5}, 0 \leq x \leq 5 \\ 0, otherwise \end{cases}$

So, the probability value of $P (x < 0)$ will be calculated as:

$P (x < 0) = 1 - P (x \geq 0)$

$= 1 - \int_{0}^{5} \frac{1}{5} d x$

$= 1 - \frac{1}{5} [x]_{0}^{5}$

$= 1 - \frac{1}{5} [5 - 0]$

$= 0$

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$f (x)$ for a continuous probability function is $1 5$ , and the function is restricted to $0 \leq x \leq 5$ . What is $P (x < 0)$ ?

Short Answer

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$f (x)$ for a continuous probability function is $1 5$ , and the function is restricted to $0 \leq x \leq 5$ . What is $P (x < 0)$ ?