What is the Cumulative Distribution Function for a Continuous Random Variable?

In summary, a random variable is a mathematical concept that represents a numerical quantity determined by chance or randomness. There are two types of random variables: discrete, which can only take on a finite or countably infinite number of values, and continuous, which can take on any value within a given range. A random variable differs from a regular variable in that it represents the outcomes of a random event, while a regular variable represents a value in an equation or formula. The probability distribution of a random variable is a function that assigns probabilities to each possible value, providing information about the likelihood of each outcome occurring. The expected value of a random variable is the average value obtained if the variable were repeated an infinite number of times, calculated by multiplying each possible value
  • #1
Dr ps
1
0
The cumulative distribution function of a continuous random variable is given
as follows:
0 0
( ) 0 5
5
1 5
X
if x
x
F x if x
x
 

   

 
a. Determine and name the density function of . [02]
b. Use both and ( ) X F x to find P(X  3) . [05]
c. Find the variance of . [03]
d. Use the method to find the probability density function of .[06]
e. Find the variance of .
 
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  • #2
The layout of the question looks completely broken.
 

What is a random variable?

A random variable is a mathematical concept used in statistics and probability theory. It represents a numerical quantity whose value is determined by chance or randomness.

What is the difference between a discrete and continuous random variable?

A discrete random variable can only take on a finite or countably infinite number of values, while a continuous random variable can take on any value within a given range.

How is a random variable different from a regular variable?

A random variable is a mathematical concept used to represent the outcomes of a random event, while a regular variable is a symbol used to represent a value in a mathematical equation or formula.

What is the probability distribution of a random variable?

The probability distribution of a random variable is a function that assigns probabilities to each possible value of the variable. It provides information about the likelihood of each outcome occurring.

What is the expected value of a random variable?

The expected value of a random variable is the average value that would be obtained if the variable were repeated an infinite number of times. It is calculated by multiplying each possible value by its corresponding probability and summing all the values together.

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