Two fair dice are rolled. Find (In tabular form) the joint and marginal probability mass functionsof X and Y when a. X is the largest value obtained on two dice and Y is the sum of the values.Compute P(Y-2X = 0); b. X is the value on the first die and Y is the larger of the two values.Compute P(Y > = X); c. X is the smallest and Y is the largest value obtained on the dice.Compute (Y > 2X). In each of three cases above, compute the joint CDF of X and Y at (sqrt(6), 2)

Here given that two fair dice are rolled. Find the joint and marginal distribution of X and Y where…

Answered: Two fair dice are rolled. Find (In…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. The joint probability mass function of X and Y is as follows: Find the marginal probability mass function of X. Round the answers to two decimal places. Find the marginal probability mass function of Y. Round the answers to two decimal places. Find µX. Find µY. Find σX . Find σY. Find Cov(X, Y). Find ρX,Y .
Two six-sided dice are rolled, and the random variable X is defined as the sum of the two numbers. Fill in the partial pdf for X.
A motorcycle drives from Moraytato Lacson and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Morayta to Lacson and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by x y 0 1 2 3 4 0 0.01 0.01 0.03 0.07 0.01 1 0.03 0.05 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 (g) Give the standard deviation of X. Answer=
A roulette wheel has thirty slots consisting of two blue, eight white, and twenty red slots. You will receive P100 if the roulette stops spinning on a blue slot, P50 on a white slot, and nothing on a red slot. Let X be the amount you will receive as shown on the slot where the roulette stops spinning. Give the probability mass function of X. O x 100 50 f(x) 2/30 8/30 20/30 100 50 f(x) 1/15 4/15 5/15 100 50 f(x) 1/15 14/15 100 50 f(x) 1/3 1/3 1/3
Three 3-sided dice are tossed. Each die has its sides labeled 0, 1, and 2. Let X denote the product of the outcomes of the threee dice. Determine the probability mass function (pmf) of X.
The table gives the joint probability distribution of the number of sports an individual plays (X) and the number of times she may get injured while playing (Y) X=1 X=2 X=3 0.12 0.08 0.15 0.06 0.05 0.05 0.10 0.03 0.15 0.15 0.04 0.02 Y=4 Y=3 Y=2 Y=1 The covariance between X and Y, oxy, is (Round your answer to two decimal places Enter a minus sign if your answer is negative) The correlation between X and Y, corr(X, Y), is (Round your answer to two decimal places Enter a minus sign if your answer is negative.) An increase in the number of sports an individual plays will tend to * the number of times she may got injured while playing
Let x be the cost ($) of an appetizer and y be the cost of a main course at a certain restaurant for a customer who orders both courses. Suppose that x and y have the following joint distribution: X 5 6 7 Find the probability mass function of x. Find the probability mass function of y. 10 .20 .10 .10 y 15 .15 .15 .10 20 .05 .10 .05
In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let Y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table: y 0.10 0.11 0.05 0.17 0.23 0.08 2 0.06 0.14 0.06 Find P(X = land Y = 0). a. Find P(X 2 land Y 1). b. C. d. Find the probability that the standard for ozone is exceeded at least once. Find the probability that the standard for particulate matter is never exceeded. e. f. Find the probability that neither standard is ever exceeded. g.

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