Continuous Probability Distribution

Continuous Probability Distribution

• The midterm grade of a random student
• The time it takes a random student to finish an assignment
• A randomly selected patient's blood pressure
• A randomly selected company's advertising budget

Probability Distribution/Density Function

• The probability that a continuous random variable will take any particular value is zero.
• i.e. $P(X=x)=0$ for any value $x$.
• The PDF of a continuous random variable cannot be expressed as a table with discrete values.
• The PDF of a continuous random variable is expressed as a function $f(x)$
• The probability $P(a<X<b)$ is calculated by finding the area under the probability density curve between the points $x=a$ and $x=b$

• Every point on the density curve has a vertical height between 0 and 1 since the probability must be a value between 0 and 1
• The total area under the density curve equals 1 since the total probability of all possible outcomes must equal 1