3. Let X represent the number that occurs when die A is tossed and Y the...
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.
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
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*).
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...
Let the variance of random variable X be 3, the variance of Y be 12, and the variance of Z be 9, and let X, Y , and Z be uncorrelated. Find V ar(4 − 2X + 3Y − 10Z).
Let x represent one number and let y represent the other number. Twice a first number decreased by a second number is 5. The first number increased by four times the second number is - 29. Use the given conditions to write a system of equations. Solve the system and find the numbers. Write a system of equations. ОА. B 3x +y = - 30 ( x + y = - 30 |2x - y = 5 x + 4y...
A fair coin is tossed n times. Let X be the number of heads in this n toss. Given X = x, we generate a Poisson random variable Y with mean x. Find Var[Y]. Answer depends on n.
Extra: Let X, Y, Z be results of three independent tosses of a fair die. (a) Find the covariance of the random variables W=2X-3Y + Z (b) Find the correlation coefficient of W and V. and V=X-2Y-Z
A coin with probability p is tossed until the first head occurs. It is then tossed again until the first tail occurs. Let X be the total number of tosses required. 1) Find the distribution function of X. 2) Find the mean and variance of X.