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7 Let Xbe a random variable whose values are the number of dots that appear on-the...
1. Determine whether or not the random variable X is a binomial randon variable. If so...
1. Determine whether or not the random variable X is a binomial randon variable. If so give the values of n and p. If not, explain why not. a. X is the number of dots on the top face of fair die that is rolled. b. X is the number of hearts in a five-card hand drawn (without replacement) from a well-shuffled ordinary deck c. X is the number of defective parts in a sample of ten randomly selected parts...
(1 point) You are to roll a fair die n = 104 times, each time observing the number of dots appearing on the topside of...
(1 point) You are to roll a fair die n = 104 times, each time observing the number of dots appearing on the topside of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i = 1,2, ..., 104 (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll...
A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The...
A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The die is fair, each face is equally likely to land upward when the die is rolled. Let X be the number of times that the number on the upward face of the die is 1. Find the mean and the standard deviation of the random variable X.
You are to roll a fair die n=123 times, each time observing the number of dots...
You are to roll a fair die n=123 times, each time observing the number of dots appearing on the topside of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i=1,2,⋯,123. (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die. μXi= (at least one decimal)...
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times ...
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
2. Assume two fair dice are rolled. Let X be the number showing on the first die and number showing on the second die. (a) Construct the matrix showing the joint probability mass function of the pair...
2. Assume two fair dice are rolled. Let X be the number showing on the first die and number showing on the second die. (a) Construct the matrix showing the joint probability mass function of the pair X,Y. (b) The pairs inside the matrix corresponding to a fixed value of X - Y form a straight line of entries inside the matrix. Draw those lines and use them to construct the probability mass function of the random variable X-Y- make...
A fair tetrahedron (four-sided die) is rolled twice. Let X be the random variable denoting the...
A fair tetrahedron (four-sided die) is rolled twice. Let X be the random variable denoting the total number of dots in the outcomes, and Y be the random variable denoting the maximum in the two outcomes. Thus if the outcome is a (2, 3) then X = 5 while Y = 3. (a) What are the ranges of X and Y ? (b) Find the probability mass function (PMF) of X and present it graphically. Describe the shape of this...
Suppose a fair die is rolled 10 times. Find the numerical values of the expectations of...
Suppose a fair die is rolled 10 times. Find the numerical values of the expectations of each of the following random variables: a). the sum of the numbers in the 10 rolls; b). the sum of the largest 2 numbers in the first 3 rolls; c). the maximum number in the first 5 rolls; d). the number of multiples of 3 in the 10 rolls; e). the number of faces which fail to appear in the 10 rolls; f). the...
Two four-sided dice, one red and one white, will be rolled. List the possible values for the following random variable. Let Y = difference between the number on the red die and the number on the white...
Two four-sided dice, one red and one white, will be rolled. List the possible values for the following random variable. Let Y = difference between the number on the red die and the number on the white die (red-white). a. Draw the probability histogram for this random variable. b. What is the most likely value of Y? c. What is the probability that the difference on the dice is negative? Use proper notation throughout. Write your answer as a decimal.
(3.) A fair six-sided die is rolled repeatedly. Let R denote the random variable representing the...
(3.) A fair six-sided die is rolled repeatedly. Let R denote the random variable representing the outcome of any particular roll. The following random variables are all discrete-time Markov chains. Specify the transition probabilities for each (as a check, make sure the row sums equal 1) (a) Xn, which represents the largest number obtained by the nth roll. (b) Yn, which represents the number of sixes obtained in n rolls.
1. Determine whether or not the random variable X is a binomial randon variable. If so give the values of n and p. If not, explain why not. a. X is the number of dots on the top face of fair die that is rolled. b. X is the number of hearts in a five-card hand drawn (without replacement) from a well-shuffled ordinary deck c. X is the number of defective parts in a sample of ten randomly selected parts...
(1 point) You are to roll a fair die n = 104 times, each time observing the number of dots appearing on the topside of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i = 1,2, ..., 104 (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll...
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
2. Assume two fair dice are rolled. Let X be the number showing on the first die and number showing on the second die. (a) Construct the matrix showing the joint probability mass function of the pair X,Y. (b) The pairs inside the matrix corresponding to a fixed value of X - Y form a straight line of entries inside the matrix. Draw those lines and use them to construct the probability mass function of the random variable X-Y- make...
(3.) A fair six-sided die is rolled repeatedly. Let R denote the random variable representing the outcome of any particular roll. The following random variables are all discrete-time Markov chains. Specify the transition probabilities for each (as a check, make sure the row sums equal 1) (a) Xn, which represents the largest number obtained by the nth roll. (b) Yn, which represents the number of sixes obtained in n rolls.
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