The random variable $ x $ has the following continuous probability distribution in the range $ 0 \leq x \leq k - 4 $ (where $ k $ is a positive number) is shown in the coordinate plane with $ x $ on the horizontal axis.### Diagram Explanation:- **Axes**: The horizontal axis represents the variable $ x $, and the vertical axis represents the function $ f(x) $.- **Line Segment**: - There is a horizontal line at the height $ \frac{k}{3} - 1.5 $ that extends from $ x = 0 $ to $ x = k - 4 $. - The line indicates a constant probability density function over this interval.- **Endpoints**: At $ x = k - 4 $, the line ends indicating the boundary of the probability distribution.### Question:What is the median of $ x $?*Answer box provided for input.*

The distribution represented in graph is a uniform distribution which is defined by the upper and lower bound of the distribution U(a,b). a is lower bound and b is upper bound. To find the value of k first compute the area under the curve which will be equal to the total probability 1. The area will be equal to multiplication of x and f(x). k3-1.5k-4=1k23-4k3-1.5k+6=1k23-8.5k3+6-1=0k2-8.5k+15=0By solving the quadratic equation, k=6 or k=2.5. So possible value of upper bound of the uniform distribution can be computed by substituting the value of k in x=k-4 x=6-4=2orx=2.5-4=-1.5 In the uniform distribution the x values are always positive, so x=2The median of uniform distribution is the point where cumulative probability is 0.5 or it can be computed directly using M=a+b2. The lower bound is a=0 and upper bound is b=2. M=0+22=1

Math

Statistics

The random variablex has the following continuous probability distribution in the range 0 < x < k – 4 (where k is a positive number) is shown in the coordinate plane with x on the horizontal axis. f(x) k - 1.5 3 k –4 What is the median of x?

The random variablex has the following continuous probability distribution in the range 0 < x < k – 4 (where k is a positive number) is shown in the coordinate plane with x on the horizontal axis. f(x) k - 1.5 3 k –4 What is the median of x?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

The random variable $ x $ has the following continuous probability distribution in the range $ 0 \leq x \leq k - 4 $ (where $ k $ is a positive number) is shown in the coordinate plane with $ x $ on the horizontal axis.

### Diagram Explanation:
- **Axes**: The horizontal axis represents the variable $ x $, and the vertical axis represents the function $ f(x) $.
- **Line Segment**:
- There is a horizontal line at the height $ \frac{k}{3} - 1.5 $ that extends from $ x = 0 $ to $ x = k - 4 $.
- The line indicates a constant probability density function over this interval.
- **Endpoints**: At $ x = k - 4 $, the line ends indicating the boundary of the probability distribution.

### Question:
What is the median of $ x $?

*Answer box provided for input.*

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