Let X represent the number that occurs when a 5-sided red die is tossed and Y the number that occurs when a 5-sided green die is tossed.
Find the variance of the random variable 7 X -Y.
Let X represent the number that occurs when a 5-sided red die is tossed and Y...
3. Let X represent the number that occurs when die A is tossed and Y the number that occurs when die B is tossed. Find the mean and variance of the random variable Z-X +3Y -5. (5pt)
Two fair 6-sided dice are tossed. Let X denote the number appearing on the first die and let y denote the number appearing on the second die. Show that X, Y are independent by showing that P(X = x, Y = y) = P(X = x) x P(Y = y) for all (x,y) pairs.
A fair coin is tossed four times and let x represent the number of heads which comes out a. Find the probability distribution corresponding to the random variable x b. Find the expectation and variance of the probability distribution of the random variable x
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.
Let random variable x represent the number of heads when a fair coin is tossed two times. a) construct a table describing probability distribution b) determine the mean and standard deviation of x (round to 2 decimal places)
math 1. Suppose that a weighted die is tossed. Let X denote the number of dots that appear on the upper face of the die, and suppose that P(X = z) = (7-2)/20 for x = 1, 2, 3, 4, 5 and P(X = 6) = 0. Determine each of the following: 116 CHAPTER 4. DISCRETE RANDOM VARIABLES (a) The probability mass function of X (b) The cumulative distribution function of X (c) The expected value of X (d) The...
help with number 4 4. Roll a die and flip a coin. Let Y be the value of the die. Let Z = 1 if the coin shows a head, and Z = 0 otherwise. Let X = Y + Z. Find the variance of X. 5. (a) If X is a Poisson random variable with = 3, find E(5*).
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.
Roll two fair four-sided dice. Let X and Y be the die scores from the 1st die and the 2nd die, respectively, and define a random variable Z = X − Y (a) Find the pmf of Z. (b) Draw the histogram of the pmf of Z. (c) Find P{Z < 0}. (d) Are the events {Z < 0} and {Z is odd} independent? Why?
(a) Consider four independent rolls of a 6-sided die. Let X be the number of l's and let y be the number of 2's obtained. What is the joint PMF of X and Y? (b) Let X1, X2, X3 be independent random variables, uniformly distributed on [0,1]. Let Y be the median of X1, X2, X3 (that is the middle of the three values). Find the conditional CDF of X1, given that Y = 0.5. Under this conditional distribution, is...