Question
In: Statistics and Probability
Consider the experiment of tossing two dice. Your random variable is D, the square of difference...
Consider the experiment of tossing two dice. Your random variable is D, the square of difference of the numbers showing on the faces of the two dice.
- Show its probability distribution in the form of a table.
- Find the mean, median and mode of the distribution.
- Find the variance of D.
- What type of skewness does the probability distribution represent?
- Is the Chebychev inequality satisfied for c=1 and c=2? Show the calculations.
Solutions
orchestra answered 1 year agoRelated Solutions
Consider the experiment of tossing two dice. Your random variable is D, the square of difference...
Consider the experiment of tossing two dice. Your random
variable is D, the square of
difference of the numbers showing on the faces of the two
dice.
Show its probability distribution in the form of a table.
Find the mean, median and mode of the distribution.
Find the variance of D.
What type of skewness does the probability distribution
represent?
Is the Chebychev inequality satisfied for c=1 and c=2? Show the
calculations.
Consider the experiment of tossing two dice. Your random variable is D, the square of difference...
Consider the experiment of tossing two dice. Your random
variable is D, the square of difference of the numbers showing on
the faces of the two dice.
Show its probability distribution in the form of a table.
Find the mean, median and mode of the distribution.
Find the variance of D.
What type of skewness does the probability distribution
represent?
Is the Chebychev inequality satisfied for c=1 and c=2? Show the
calculations.
Let a random experiment consist of tossing two fair six sided dice. Let x be the...
Let a random experiment consist of tossing two fair six sided
dice. Let x be the minimum number shown on the dice.
Determine the closed form PMF of x.
Hint: Creating a chart for all possible combinations of the two
rolls may be helpful.
let x be the random variable in rolling two dice denotes the absolute difference between die...
let x be the random variable in rolling two dice denotes the
absolute difference between die faces .
(i) find the probability distribution f(x) and cumulative
distribution F(x) .
ii) plot f(x) and F(x)
iii) find the mean and variance of x and of g(x) = 3x + 7
Consider rolling two dice and let (X, Y) be the random variable pair defined such that...
Consider rolling two dice and let (X, Y) be the random variable
pair defined such that X is the sum of the rolls and Y is the
maximum of the rolls.
Find the following:
(1) E[X/Y]
(2) P(X > Y )
(3) P(X = 7)
(4) P(Y ≤ 4)
(5) P(X = 7, Y = 4)
Our experiment is to roll 2 dice 900 times. The random variable, X, is the number...
Our experiment is to roll 2 dice 900 times. The random variable,
X, is the number of times that the two dice add up to either 7 or
11. Find E(X), Var(X), and E(X^2).
Assuming that the Central Limit Theorem applies, AND that the
standard deviation is exactly 12.5, AND not bothering with the
half-unit correction, find:
P(X>225)
P(X<175)
Consider the experiment of rolling two dice and the following events: A: 'The sum of the...
Consider the experiment of rolling two dice and the following
events:
A: 'The sum of the dice is 8'
and B: 'The first die is an odd number' and
C: "The difference (absolute value) of the dice is
2"
Find (a) p(A and B) (HINT: You cannot
assume these are independent events.)
(b) p(A or
B)
(c) Are
A and B mutually exclusive events? Explain.
(d) Are A and B independent events?
Explain.
(e) Are B and C independent events?
Explain.
Consider a random experiment of rolling 2 dice. What is probability of rolling a sum larger...
Consider a random experiment of rolling 2 dice. What is
probability of rolling a sum larger than 9? Select the best answer.
A. 0.5
B. 0.1667
C. 0.2333
D. None of the above
I. Consider the random experiment of rolling a pair of dice. Note: Write ALL probabilities as...
I. Consider the random experiment of rolling a pair of dice.
Note: Write ALL probabilities as reduced fractions or whole numbers
(no decimals).
1) One possible outcome of this experiment is 5-2 (the first die
comes up 5 and the second die comes up 2). Write out the rest of
the sample space for this experiment below by completing the
pattern:
1-1
2-1
1-2
1-3
1-4
1-5
1-6
2) How many outcomes does the sample space contain?
_____________
3) Draw...
I. Consider the random experiment of rolling a pair of dice. Note: Write ALL probabilities as...
I. Consider the random experiment of rolling a pair of dice.
Note: Write ALL probabilities as reduced fractions or whole numbers
(no decimals).
1-1
2-1
3-1
4-1
5-1
6-1
1-2
2-2
3-2
4-2
5-2
6-2
1-3
2-3
3-3
4-3
5-3
6-3
1-4
2-4
3-4
4-4
5-4
6-4
1-5
2-5
3-5
4-5
5-5
6-5
1-6
2-6
3-6
4-6
5-6
6-6
2) How many outcomes does the sample space contain?
_____36________
3)Draw a circle (or shape) around each of the following events...
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