Probability distribution and finding the median

In summary, the problem asks to compute the median of a distribution with a density function given by f(x)={(x^3)/4 0<x<2 {0 otherwise. The equation int f(x)dx from m to inf =1/2 is used to find the median. The issue of m not being defined is resolved by noting that f(x)=0 for x>2 and x<0. Therefore, the integral converges and the problem can be solved.
  • #1
Painguy
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0

Homework Statement


Suppose that x measures the time (in hours) it takes for students to complete an exam. All students are done within 2 hours and the density function for x is given by

f(x)={(x^3)/4 0<x<2
{0 otherwise

Compute the median of this distribution. (Give an exact answer.)


Homework Equations



int f(x)dx from m to inf =1/2

The Attempt at a Solution



I'm not sure what m is supposed to be, and because of that I'm completely lost. It looks like the integral doesn't even converge. How do I go about this problem?
 
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  • #2
Painguy said:

Homework Statement


Suppose that x measures the time (in hours) it takes for students to complete an exam. All students are done within 2 hours and the density function for x is given by

f(x)={(x^3)/4 0<x<2
{0 otherwise

Compute the median of this distribution. (Give an exact answer.)

Homework Equations



int f(x)dx from m to inf =1/2

The Attempt at a Solution



I'm not sure what m is supposed to be, and because of that I'm completely lost. It looks like the integral doesn't even converge. How do I go about this problem?

Yes, it does converge. f(x)=0 for x>2 and x<0. You aren't really integrating to infinity. Now get started.
 

1. What is a probability distribution?

A probability distribution is a mathematical function that describes the likelihood of different outcomes or values occurring in a given situation. It shows how the total probability is divided among all the possible outcomes.

2. Why is it important to understand probability distributions?

Understanding probability distributions is important because it allows us to make predictions about the likelihood of certain events or values occurring. It also helps us to analyze and interpret data, and make informed decisions based on the probability of different outcomes.

3. What is the difference between a discrete and a continuous probability distribution?

A discrete probability distribution deals with discrete random variables, which can only take on a limited number of possible values. Examples include rolling a die or flipping a coin. A continuous probability distribution deals with continuous random variables, which can take on any value within a certain range. Examples include height or weight measurements.

4. How is the median calculated in a probability distribution?

The median in a probability distribution is the middle value or the value that separates the lower and upper halves of the distribution. To calculate it, the values in the distribution are first arranged in ascending or descending order, then the middle value is determined. If there is an even number of values, the median is the average of the two middle values.

5. Can the median be used to describe a skewed distribution?

Yes, the median can still be used as a measure of central tendency in a skewed distribution. However, it may not be the most representative measure, as it can be influenced by extreme values. In this case, the median should be interpreted along with other measures such as the mean and mode to get a better understanding of the distribution.

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