Explore BrainMass
Share

Continuous Random Variable and Probability Density Function

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Let X denote a continuous random variable with probability density function f(x) = kx^3/15 for 1≤ X ≤ 2.

a. Determine the value of the constant k.

b. Determine the probability that X > 1.5.

c. Determine the cumulative distribution function F(x) and state the values of F(x) at x = 0.5, 1.5, and 2.5.

© BrainMass Inc. brainmass.com October 16, 2018, 8:31 pm ad1c9bdddf
https://brainmass.com/statistics/probability-density-function/continuous-random-variable-probability-density-function-152421

Solution Summary

This solution used the probability density function to determine the value of 'k', the probability that X>15 and the cumulative distribution function. It also calculates the values of F(x) at 0.5, 1.5 and 2.5 with all steps shown.

$2.19
Similar Posting

Probability, Random Variables, Joint Density Functions, Cumulative Density Functions and Projection Graphs (12 Problems)

1. Given the joint density function for the random variables X and Y as

The marginal distribution for the random variable X is

Answer:

2. Given the joint density function for the random variables X and Y as

The marginal distribution for the random variable Y is

Answer:

3. The following represents the cumulative distribution function for a random variable X.

From the graph, find .

Answer: 0.4

4. The life span in hours for an electrical component is a random variable X with cumulative distribution function

Determine the probability density function for X.

Answer:

5. Let X be the random variable for the life in hours for a certain electronic device. The probability density function is

The expected life for a component is

Answer: 2000 hours

6. The life, X in hundred of hours, of a certain battery has the following density function

What is the average life of the battery?
Answer: 200 hours

7. The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution

What is the expected or average time between successive speeders?

Answer: 0.125 hours

8. The probability distribution of X, the number of defects per 100 yards of a fabric is given by
x 0 1 2 3 4
f(x) 0.45 0.35 0.14 0.05 0.01

The variance for X is
Answer: 0.8476

9. The following represents the projection graph for a probability distribution f(x) of a random variable X.

What is the value for the variance of X?

Answer: 1

10. The following represents the cumulative distribution function for a random variable X.

What is the expected value of X?

Answer: 2.2

11. The life span in hours for an electrical component is a random variable X with cumulative distribution function

Determine the expected life span for an electrical component.

Answer: 100

12. The life span in hours for an electrical component is a random variable X with cumulative distribution function

Determine the variance for the life span for an electrical component.

Answer: 10000

keywords: cdf, pdf

View Full Posting Details