Probability Distributions
Is this distribution represent a probability distribution.
X 1 2 3 4 5
P(x) 1/7 2/7 2/7 3/7 2/7
No, the sum is greater than 1
There are six playing cards placed face down in a box. They are the 4 of diamonds, the 5 of hearts, the 2 of clubs, the 10 of spades, the 3 of diamonds, and the 7 of hearts. A person selects a card. Find the expected value.
E(x)=
= 5.2
The number of calls received per day at a crisis hot line is distributed as follows:
x 30 31 32 33 34
P(x) 0.05 0.21 0.38 0.25 0.11
Find the variance and standard deviation.
Variance= 1.1
Standard Deviation = 1.0
A random variable is one that can take on multiple values.
True
Is the distribution a probability distribution.
x 3 6 9 12 15
P(x) 0.3 0.5 0.1 0.08 0.02
Yes
A person selects a card from an ordinary deck of cards. If it is a black card, she wins $2. If it is a red card between or including 3 and 7, she wins $10. If it is a red face card, she wins $25; and if it is a black jack, she wins an extra $100. Find the expectation of the game.
E(x)=
= $9.65
A history class has 75 members. If there is a 12% absentee rate per class meeting, find the variance and standard deviation of the number of students who will be absent from each class.
variance = 7.9
stand. Dev. = 2.8
Continuous random variables are obtained from data that can be measured rather than counted.
true
Is the distribution a probability distribution?
x 50 75 100
P(x) 0.5 0.2 0.3
Yes
The number of calls received per day at a crisis hot line is distributed as follows:
x 30 31 32 33 34
P(x) 0.05 0.21 0.38 0.25 0.11
Find the mean.
mean = 30(.05) + 31(.21) + 32(.38) + 33(.25) + 34(.11)
= 32.2
During a recent CD sale at Matt's Music Store, the number of Cd's customers purchased was distributed as follows:
x 0 1 2 3 4
P(x) .10 .23 .31 .27 .09
Find the variance and standard deviation.
variance = 1.3
stand dev = 1.1
Macaroni and cheese is your favorite food.
True/False
Which value would be needed to complete the following probability distribution?
x -2 -1 0 1 2
P(x) .38 .26 .16 .05 ?
?=1- (.38+.26+.16.05)
= .15
The ____________ of a discrete random variable of a probability distribution is the theoretical average of the variable.
mean/ expected value
If the standard deviation of a probability distribution is 6.25, the variance is 2.30.
False.
What are the 2 conditions needed for a probability distribution to be valid ?
The sum of probabilities should be equal to 1
all probabilities should be between 0 and 1