1. PROBABILITY DISTRIBUTIONS

2. Probability Distribution  Suppose we toss a fair coin 3 times. What is the sample space?  What is the probability for each possible outcome?  Now let’s define X = number of heads obtained. Value:0123 Probability:

3.  What is the probability that we get at least one head in three tosses of the coin?

4. Apgar Scores: babies’ health at birth  In 1952, Dr. Virginia Apgar suggested five criteria for measuring a baby’s health at birth: skin color, heart rate, muscle tone, breathing, and response when stimulated. She developed a 0-1-2 scale to rate a newborn on each of the five criteria. Babies are usually tested at one minute after birth and again at five minutes after birth. A baby’s Apgar scores is the sum of the ratings on each of the five scales, which gives a whole number value from 0 to 10.  Doctors decided that Apgar scores from 7 to 10 indicate a healthy baby. What is the probability that a randomly selected baby is healthy? Value:012345678910 Probability 0.0010.0060.0070.0080.0120.0200.0380.0990.3190.4370.053

5. Expected Value  On a roulette wheel, there are 38 slots numbered 1 through 36, plus 0 and 00. Half of the slots from 1 to 26 are red; the other half are black. Both the 0 and 00 slots are green. A player can place a simple $1 bet on either red or black. If the ball lands in a slot of that color, the player gets the original dollar back, plus an additional dollar for winning the bet. If the ball lands in a different colored slot, the player loses the dollar bet to the casino. What is the player’s average gain?

6. Expected Value  Found by multiplying each possible value of the variable by its probability and then summing over all possible outcomes.

7. Household Size  According to the Census Bureau, the number of people X in a randomly selected U.S. household follows the probability distribution given in the table below:  Calculate the P(X>2)  Find the expected value of X and explain what it tells you. Number of people x: 1234567 Probability: 0.250.320.170.150.070.030.01