Transcript 8.0 Probability Distribution

STATISTICS
“Probability Distribution”
8.0 Counting Principles & Probability Distribution
8.0 Probability Distribution
• Random Variables
– The outcomes of these experiments are
considered random variables
– A random variable is an outcome that takes on
a numerical value as a result of experiment.
The value of the random variable is often
denoted by x.
E.g. P[x=1] = 1/6
8.0 Probability Distribution
• Random Variables
– Random variables are categories into 2 type:
a)Continuous random variables
(The result of a measurement on a continuous number scale)
b)Discrete random variables
(The result of a counting outcomes rather than measuring them)
8.0 Probability Distribution
Continuous random variables
1.
A random variable is continuous if it can assume
any numerical within an interval as a result of
measuring the outcome of an experiment.
2.
E.g. The weight of Ali measured daily for the
month →values CRV could be 80kg, 85kg, 81kg..
8.0 Probability Distribution
Discrete random variables
1.
A random variable is discrete if it is limited to
assuming only specific integer values as a result of
counting the outcome of an experiment.
2.
E.g. The number of meal of Ali take in a month for
him diet program →values DRV could be 2,1, 3…
8.0 Probability Distribution
• Continuous vs Discrete
CRV:
1) The amount of local rainfall, in inches this month
2) The length of time a customer required at a checkout
lane in the grocery store
3) The speed of a vehicle travelling on the inter-state
measured by a radar gun
DRV:
1) The number of days during the month in which it
rained
2) The number of customers standing in line waiting to
check out at the grocery store
3) The number of cars that were found driving faster
than the speed limit during the past hour
8.0 Probability Distribution
Probability Distribution
1.
A probability distribution is a listing of all the
possible outcomes of an experiment along with
the relative frequency/probability of each
outcome.
2.
Probability distribution play a major role in the use
of inferential statistics.
8.0 Probability Distribution
Discrete Probability Distribution
1.
2.
A listing of all the possible outcomes of an
experiment for a discrete random variable along
with the relative freq/probability of each
outcome is called a discrete probability
distribution
n
Mean of a DPD = μ = ∑
i =1
Xi * P[Xi]
μ = the mean of the DPD
Xi = the value of random variable
P[Xi] = the probability of the ith outcome
n = the no. of outcome in the distribution
8.0 Probability Distribution
Discrete Probability Distribution
n
3.
The variance of DFD = σ² =
∑
(Xi - mean)² * P[Xi]
i =1
4.
The std deviation of a DPD = σ = √ σ²
σ² = the variance of the DPD
μ = the mean of the DPD
Xi = the value of random variable
P[Xi] = the probability of the ith outcome
n = the no. of outcome in the distribution
8.0 Probability Distribution
• TRY THIS!!
A survey of 500 passengers was conducted to find how
many luggages were brought along during their flight trip
to their respective destinations. The following table
summarizes the results:
(xi)
Freq
0
25
1
185
2
137
3
98
4
45
5
10
a) Develop a probability distribution for this data
b) Calculate the mean, variance and standard deviation.
8.0 Probability Distribution
• TRY THIS!!
SPCA conduct a survey of 450 families to find how many
cats were owned by each respondent. The following table
summarizes the results:
(xi)
Freq
0
137
1
160
2
112
3
31
4
10
a) Develop a probability distribution for this data
b) Calculate the mean, variance and standard deviation.
Quiz 7