Finding constant in Probability density function.

In summary, a probability density function (PDF) is a mathematical function used to describe the probability distribution of a continuous random variable. It includes a constant, which is a scaling factor that ensures the total area under the curve is equal to 1. This constant is found by integrating the function over its entire range and setting the result equal to 1. It is important in calculating the probability of specific ranges of values for the variable and must always be positive to properly represent probabilities between 0 and 1.
  • #1
sid9221
111
0
A continuous random variable X has pdf:

[tex] f_X(x)=\left \{ k(x+3), 0\leq x\leq 1\right \} [/tex]

0 otherwise.

Find k.

I solved the integral (from 0..1) and solved for the result equal to 1.

Hence I got k=2/7.

Is this the right way to proceed as the question continues and I want to check if I'm starting correctly
 
Physics news on Phys.org
  • #2
yep, you just want to normalise to 1
 
  • #3
What do you mean normalize to 1 ?

It was 7/2k=1
So k=2/7

?
 
  • #4
sid9221 said:
What do you mean normalize to 1 ?

It was 7/2k=1
So k=2/7

?

Normalizing means making [tex]\int_0^1 f_X(x) \, dx = 1.[/tex]

RGV
 

FAQ: Finding constant in Probability density function.

What is a probability density function (PDF)?

A probability density function (PDF) is a mathematical function that describes the probability distribution of a continuous random variable. It provides the relative likelihood of observing a specific value or range of values for the variable.

2. What is the constant in a probability density function?

The constant in a probability density function is a scaling factor that ensures that the total area under the curve is equal to 1. This constant is necessary because the probability of any specific value for a continuous random variable is infinitesimal, so the area under the curve represents the probability of a range of values instead.

3. How do you find the constant in a probability density function?

The constant in a probability density function can be found by integrating the function over its entire range and setting the result equal to 1. This allows you to solve for the constant and determine its value.

4. What is the purpose of finding the constant in a probability density function?

The constant in a probability density function is important because it allows us to calculate the probability of a specific range of values for a continuous random variable. Without this constant, the probability density function would not provide meaningful information about the likelihood of different outcomes.

5. Can the constant in a probability density function ever be negative?

No, the constant in a probability density function must always be positive. This is because the function represents a probability distribution, and probabilities cannot be negative. The constant ensures that the function is properly scaled to represent probabilities between 0 and 1.

Similar threads

Probability density function of Z=X+Y and Z=XY
Replies
19
Views
3K
Finding marginal distribution of 2d of probability density function
Replies
6
Views
1K
Determine marginal densities and distributions from joint density
Replies
7
Views
785
Probability Density Functions: Transformation of Variables
Replies
3
Views
1K
Finding Probability Density Functions for Independent Random Variables
Replies
2
Views
2K
Probability density function for a given problem
Replies
4
Views
1K
Solve this problem that involves a probability density function
Replies
8
Views
1K
Proving piecewise function is k-differentiable
Replies
5
Views
960
Probability Density Function problem
Replies
4
Views
2K
Probability Density of ##x## (Wiener Process)
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top