Discrete vs Continuous Probabilities

Tuesday, 10/1
➢ Discrete random variable-takes on a finite number of values; cannot be a fraction
➢ Continuous random variable-takes on any of the countless numbers on a line interval
→ A variable is random if the value that x takes on is a chance/random outcome


Example
➢ Identify the type of variable for...
→ Time taken for a student to register for Fall term; continuous
→ Number of text messages received on one randomly chosen day; discrete
→ Number of miles a vehicle can drive on a full tank; continuous
→ Number of people who voted in an election; discrete


➢ Probability distribution-assignment of probabilities to each distinct value of a discrete
random variable or to each interval of values on a continuous random variable
→ Sum of all assigned probabilities must equal 1


For discrete probability distributions:
➢ Mean: µ=ΣxP(x); µ is the mean or expected value of x
➢ Standard deviation: δ=√Σ(x-µ)2P(x)


Example

# of times ad heard Percentage of P(x) xP(x)
on radio buyers/purchasers
1 27 0.27 0.27
2 31 0.31 0.62
3 18 0.18 0.54
4 9 0.09 0.36
5 15 0.15 0.75
→ µ = ΣxP(x) = 0.27 + 0.62 + 0.54 + 0.36 + 0.75 = 2.54
→ δ = √Σ(x-µ)2P(x) = √1.869 = 1.37



→ Complete the table:

Frequency P(x) xP(x)