Key Concepts
mathematical function that describes the likelihood of a continuous random variable
What is Probability Density Function?
f(x)=kx for 0≤x≤3
(a) Find value k
(b) Find P(1≤X≤2)
(a) k=2/9
(b) 1/3
f(x)=0.1xfor 0<x<10
Is this a probability density function?
Answer: no because it equals to 5
a random variable that can take on an uncountable infinite number of possible values within a given range (an interval or set of intervals) on the real number line
What is Continuous Random Variable?
f(x)=kx for 0≤x≤2
(a) Find k
(b) Find P(0.5≤X≤1.5)
(a) 1/2
(b) 1/2
f(x)=0.2xfor 0<x<5
Is this a Probability Density Function?
Answer: no because this equals to 2.5
What must always be true for a probability density function?
f(x)≥0and∫−∞∞f(x)dx=1
f(x)=kx(2−x),0≤x≤2
(a) Find k
(b) Find P(0.5≤X≤1)
(a) k=3/4
(b) 11/32
f(x)=0.25x(4−x),0≤x≤4
Is this a Probability Density Function?
Answer: No because it equals to 8/3