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Q1. (15') (Random Variables) There is an experiment of throwing a six-sided die. Let X be...
Consider the experiment of rolling six six-sided dice. Let Yi each be random variables given by the following functions of the outcomes in the experiment described above. For each of these new random variables Yi given below, describe (1) the new sample space associated with Yi (i.e., SYi = Yi(S)) and (2) the Probability function P (Yi = k) for value of k in SYi . (a) Y1 is the number of even integers in the sequence. (b) Y2 is...
(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.
Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y], rounded to nearest .XX.
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.What is P(A), the probability that the six-sided die is an even number?What is P(B), the probability that the four-sided die is an odd number?What is P(A...
In this experiment, both a fair four-sided die and a fair six-sided die are rolled (these dice both have the numbers most people would expect on them). Let Z be a random variable that represents the absolute value of their difference. For instance, if a 4 and a 1 are rolled, the corresponding value of Z is 3. (a) What is the pmf of Z? (b) Draw a graph of the cdf of Z
dice is unbiased. Throws independent. Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y] rounded to nearest .xx.
5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2)
you repeatedly roll an ordinary six sided die five times. Let X equal the number of times you roll the die. For example (1,1,2,3,4) then x =4 Find E[X]
A random experiment consists of throwing two three-sided dice (show- ing the numbers 1, 2, 3). Let Y be the random variable which records the product of the pair of numbers showing on the dice. (i) Write down the range RY of Y . (ii) Determine the probability distribution of Y . (iii) Calculate E(Y ) and V (Y ).
b) Find Var(X) 5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2) B SEIKI