Consider the continuous probability density functi

Questions: Consider the continuous probability density function defined by y=4 on -0.05 ≤ x ≤ 0.2. Compute the following probabilities. P(X<0.15)= P(X>0.15)= P(-0.05<X<0.1)=

Transcript text: Consider the continuous probability density function defined by $y=4$ on $-0.05 \leq x \leq 0.2$. Compute the following probabilities. \[ P(X<0.15)= \] $\square$ \[ P(X>0.15)= \] $\square$ \[ P(-0.05

Solution

Solution Steps

Step 1: Calculate P(X < 0.15)

The probability P(X < 0.15) is the area under the density function from x = -0.05 to x = 0.15. Since the height of the density function is y = 4, the area is given by $P(X < 0.15) = 4 * (0.15 - (-0.05)) = 4 * 0.2 = 0.8$

Step 2: Calculate P(X > 0.15)

The probability P(X > 0.15) is the area under the density function from x = 0.15 to x = 0.2. The area is given by $P(X > 0.15) = 4 * (0.2 - 0.15) = 4 * 0.05 = 0.2$

Step 3: Calculate P(-0.05 < X < 0.1)

The probability P(-0.05 < X < 0.1) is the area under the density function from x = -0.05 to x = 0.1. The area is given by $P(-0.05 < X < 0.1) = 4 * (0.1 - (-0.05)) = 4 * 0.15 = 0.6$