Statistical Methods
Discrete Probability Distribution
Q.1
Categorize each of the following as continuous or discrete. The random variables are:
(a) A is ‘the age in completed years of the first person I see wearing a hat'.
(b) B is ‘the length of the next car to enter the car park'.
(c) ) C is ‘how many cows I will see before I reach Iowa?'
(d) D is ‘the date next July of the day with the highest temperature'.
Q.2.
Let X=number of heads obtained when tossing a fair coin 3 times.
(a) Create a probability distribution table for possible values of X
X
P(X=x)
(b) What is the expected number of heads, E(X)?
(c) What is the variance?
Q.3
The random variable X has the probability distribution shown
|
X
|
1
|
2
|
3
|
4
|
5
|
|
P(X=x)
|
7c
|
5c
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4c
|
3c
|
c
|
(a) Find the value of c (Hint: Use the fact--- total probability=1)
(b) Calculate the mean and variance.
Q.4
Mr. A plays a die game by throwing a die. He wins $4 if he throws 1, wins $6 if he throws 6 and loses $2 if he throws other numbers. What is his expected loss or win per game? If he plays the game 150 times, how much he will win or lose?