Question

Let x be a continuous random variable over [a, b] with probability density function f. Then the median of the x-values is that number m for m [ f(x) dx = 1/21 which Find the median. a 1 f(x) = x, [0, 4] A. 2√2 B. 2 O C. O 3 NW 2 D. 4

Answer 1

Explanation:

To find the median of the continuous random variable with the given probability density function, we need to find the value of m such that the integral of f(x) from a to m is equal to 1/2.

In this case, the probability density function f(x) = x, and the interval is [0, 4].

To find the median, we need to solve the equation:

∫[a to m] f(x) dx = 1/2

∫[a to m] x dx = 1/2

Now, let's integrate x with respect to x:

[1/2 * x^2] [a to m] = 1/2

(1/2 * m^2) - (1/2 * a^2) = 1/2

Since the interval is [0, 4], we have a = 0 and m = 4.

Substituting the values, we get:

(1/2 * 4^2) - (1/2 * 0^2) = 1/2

(1/2 * 16) - (1/2 * 0) = 1/2

8 - 0 = 1/2

8 = 1/2

Since this is not a valid equation, there is no value of m that satisfies the equation. Therefore, there is no median for this given probability density function and interval.