Question

3.Answer the following in the space provided: a) The continuous randous variable x has probability density function of f(x) given by F(x)=3/8(x+2)² -2≤x≤0 0 elsewhere Find the value that separates the lowest 25% from the rest

Answer 1

The value that separates the lowest 25% from the rest of the data in a continuous random variable 'x' with the given probability density function is approximately -1.5.

Step-by-step explanation:

In this question, you are essentially being asked to find the lower quartile or the 25th percentile of a continuous random variable x with a given probability density function (PDF). The 25th percentile is the value below which 25% of the observations lie. This means you need to solve the following integral equation for x:

∫ from -2 to x [3/8(x+2)² dx] = 0.25

The integrated function is F(x) = (x+2)³/4 from -2 to x. Substituting x = 25th percentile into F(x) gives the equation (25th percentile + 2)³/4 - 1 = 0.25

Solving this equation for the 25th percentile gives x = -8^(1/3) - 2 ≈ -1.5

So, the value that separates the lowest 25% from the rest is approximately -1.5.

Learn more about 25th Percentile