s default My Courses CRN 40938 Chapter 5 HW - Continuous Random Variables Current score: +Å Category: Homework 0/50 points 1) 2 3 4 5 6 7 8 9 10 Current learning objective: Continuous Probability Functions Question 1 Practice similar questions Score: 0 of 5 points Consider the continuous probability density function defined by $$ f(x)=5 $$ on $$ 0 \leq x \leq \frac{1}{5} $$. Then, $$ P(0.18

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To solve the probability $$ P(0.18 < X < 0.2) $$ for the continuous random variable $$ X $$ with the probability density function $$ f(x) = 5 $$ on the interval $$ 0 \leq x \leq \frac{1}{5} $$ (which is $$ 0 \leq x \leq 0.2 $$), follow these steps:

1. **Understand the Distribution**:
   - Since $$ f(x) = 5 $$ is constant on $$ [0, 0.2] $$, $$ X $$ is uniformly distributed over this interval.

2. **Set Up the Integral**:
   - The probability $$ P(a < X < b) $$ for a uniform distribution is given by:
     $$
     P(a < X < b) = \int_{a}^{b} f(x) \, dx
     $$
   - Here, $$ a = 0.18 $$ and $$ b = 0.2 $$.

3. **Calculate the Probability**:
   $$
   P(0.18 < X < 0.2) = \int_{0.18}^{0.2} 5 \, dx = 5 \times (0.2 - 0.18) = 5 \times 0.02 = 0.1
   $$

So, the probability $$ P(0.18 < X < 0.2) $$ is **0.1**.

**Answer:**  
0.1
The probability $$ P(0.18 < X < 0.2) $$ is **0.1**.

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