1. Chapter 16 Random Variables
Ashlynn Lamb 2nd

2. Random Variable
Random variable assumes a value based on the outcome of a random event.
X denotes random variable
x denotes a particular value of a random variable
Discrete random variables take one of a finite number of distinct outcomes
Continuous random variables take any numeric value within a range of values

3. Probability Model probability model:
collection of all possible values of a random variable
probabilities that the values occur.
Of particular interest:
the value we expect a random variable to take on, notated μ or E(X) for expected value

4. Variance and SD
multiply each possible value by the probability that it occurs, and find the sum
Square the variance

5. Changing a random variable by a constant
Adding/subtracting a constant from data shifts the mean but doesn’t change the variance or standard deviation:
E(X ± c) = E(X) ± c Var(X ± c) = Var(X)
multiplying each value of a random variable by a constant multiplies the mean by that constant and the variance by the square of the constant:
E(aX) = aE(X) Var(aX) = a2Var(X)

6. Adding/Subtracting random variables
The mean of the difference of two random variables is the difference of the means.
E(X ± Y) = E(X) ± E(Y)
If the random variables are independent, the variance of their sum or difference is always the sum of the variances.
Var(X ± Y) = Var(X) + Var(Y)

7. #35
In exercise 33, we poured a large and a small bowl of cereal from a box. Suppose the amount of cereal that the manufacturer puts in the boxes in a random variable with mean of 16.2 ounces, and a standard deviation 0.1 ounces
find the expected value of cereal left in the box
find the standard deviation
what is the probability the box has more than 13 ounces

11. #37
In the 4X100 medley relay event, four swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times their swimmers have posted. Mean and SD are as shown:
backstroke, M=50.72, SD= .24
breaststroke, M=55.51, SD= .22
butterfly, M=49.91, SD= .25
freestyle, M=44.91, SD= .21

12. #37 cont.
Find the mean and standard deviation for the relay team’s total time in this event
The team’s best time so far this season was 3:19.48 ( seconds.) Do you think the team is likely to swim faster than this at the conference championship? Explain.