Probability Distributions. Random Variables * Discrete Probability Distributions * Mean, Variance, and Standard Deviation * Expected Value. Fill in the blanks 1 – 3. 1. Random Variable: A count or an \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ of a probability experiment. (Uses numerical values). outcome.
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Random Variables * Discrete Probability Distributions * Mean, Variance, and Standard Deviation * Expected Value
1. Random Variable: A count or an ________________ of a probability experiment. (Uses numerical values)
2. Discrete random variable: Has a finite or __________________ number of possible outcomes that can be listed.
3. Continuous random variable: Has a _____________ number of possible outcomes, represented by an interval on the number line.
5. Mean of a discrete random variable: Each probability of x is __________ by its corresponding probability and the products are added.
*Mean values may be bigger than 1 since they are for more than one person!
6. Variance of a discrete random variable is
7. Standard Deviation is
8. Expected Value: A ____________ random variable is equal
to the mean of the random variable.
Expected value = (note that the mean
and expected values are the same!)
Determine the missing probability value
NO! it adds up to 1.1
Example #3 Is the following a probability distribution? ______________
Hint: Use the lists in your calculator!
b) Find the mean _______________________
c) Find the variance ___________________
d) Find the standard deviation _____________________
e) A household on average has _________ dogs with a standard deviation of ________________.
Note, if it is a nice dog I want the front half!
A charity organization is selling $4 raffle tickets part of a fund-raising program. The first prize is a boat valued at $3150, and second prize is a camping tent valued at $450. The rest of the prizes are 15 - $25 gift certificates. The number of tickets sold is 5000. Find the expected net gain to the player for one play of the game. Is the players expected to win or to lose?