noreturn2 said:Homework Statement
f(x) = (3/4)(-x^2 + 6x - 8) for 2 < x < 4 (0 elsewhere)
A) Find F(x)
integral 2 to 4 ((3/4)(-x^2 + 6x - 8))dx
B) Use F(x) to find P(3 < X < 3.5)
integral 3 to 3.5 ((3/4)(-x^2 + 6x - 8))dx
11/32
C) Use F(x) to find P(X > 3.5)
1-( P(3 < X < 3.5)) = 21/31
D) Find E(X).
integral 2 to 4 (x*(3/4)(-x^2 + 6x - 8))dx = 3
E) Find the standard deviation of X.
integral 2 to 4 (x^2(3/4)(-x^2 + 6x - 8))dx E[x^2)-E[x] = sqrt(6.2)= 2.48
Continuous probability is a branch of mathematics that deals with the likelihood of an event occurring within a continuous range of values. It is used to model and analyze real-world situations where outcomes can take on any value within a given range.
Discrete probability deals with events that have a finite or countable number of outcomes, while continuous probability deals with events that have infinite possible outcomes within a range of values. Additionally, discrete probabilities are represented by discrete probability distributions, while continuous probabilities are represented by continuous probability distributions.
A probability distribution is a function that assigns probabilities to the possible outcomes of a random variable. In the case of continuous probability, this function is called a continuous probability distribution and is represented by a curve rather than a table.
Continuous probability is calculated by finding the area under the curve of a continuous probability distribution. This can be done using integration techniques such as the definite integral or by using statistical software.
Continuous probability is used in many fields, including physics, engineering, economics, and finance. Some common applications include predicting stock prices, analyzing risk in insurance, and modeling weather patterns.