Probability distribution for continuous random variables, Mathematics

Probability Distribution for Continuous Random Variables

In a continuous distribution, the variable can take any value within a specified range, e.g. 2.21 or 1.64 compared to the specific values taken by a discrete variable e.g 1 or 3. The probability is represented by the area under the probability density curve between the given values.

The uniform distribution, the normal probability distribution and the exponential distribution are examples of a continuous distribution

-           The normal distribution is a probability distribution which is used to determine probabilities of continuous variables

Examples of continuous variables are

  • Times
  • Capacity Heights
  • Weights
  • Distances
  • e.t.c

- Generally continuous variables are those that can be measured by utilizing the suitable units of measurement.

- specified are the properties of the general distribution

1. The sum of area under the curve is = 1 which is equivalent to the maximum value of probability

701_Probability Distribution for Continuous Random Variables.png

2. The line of symmetry divides curve into two equal halves

3. The two ends of the general distribution curve continuously approach the horizontal axis however they never cross it

4. The values of the mean, mode and median all each are equal

NB: The above distribution curve is referred to as general probability distribution curve since if a frequency distribution curve is plotted from measurements of a specified sample drawn from a general population then a graph similar to the normal curve must be acquired.

- It should be noted that 68 percent of any population lies in one standard deviation, ±1σ

- 95 percent lies in two standard deviations ±2σ

- 99 percent lies in three standard deviations ±3σ

Whereas σ = standard deviation

182_Probability Distribution for Continuous Random Variables 2.png

Posted Date: 2/20/2013 6:35:30 AM | Location : United States

Related Discussions:- Probability distribution for continuous random variables, Assignment Help, Ask Question on Probability distribution for continuous random variables, Get Answer, Expert's Help, Probability distribution for continuous random variables Discussions

Write discussion on Probability distribution for continuous random variables
Your posts are moderated
Related Questions
The sides of a triangle are x^(2 )+x+1, 2x+1,x^2-1, prove that the largest angle is 120 degrees, and find range of x. Ans) The biggest side is x^(2) + x + 1 so findout the angl

Michael scored 260 points during his junior year on the school basketball team. He scored 20% more points during his senior year. How many points did he score during his senior yea

How do you find the area of a circle given the diameter?

Evaluate following limits. Solution Let's begin with the right-hand limit.  For this limit we have, x > 4  ⇒          4 - x 3   = 0      also, 4 - x → 0  as x → 4

Solve the linear equation: The equation relating the pressure that is denoted by P, to the force, F & the area, A, over which the force is applied is P =F/A.  Solve this equat

Q. Show Inverse Trigonometric Functions? Ans. Many functions, including trig functions, are invertible. The inverse of trig functions are called ‘inverse trig functions'.

Classical Probability Consider the experiment of tossing a single coin. Two outcomes are possible, viz. obtaining a head or obtaining a tail. The probability that it is a tail

Describe differance between Mean vs. Mode ? Every set of numbers or data has a mean and a mode value. The mean is the average value of all the numbers in the set. The mode is t

Example of Graphing Equations: Example: By using the above figure, find out the distance traveled if the average speed is 20 mph and the time traveled is 40 minutes. T