A standard deck of 52 cards is thoroughly shuffled and laid face-down. You flip over the cards one by one. Let the random variable X1 be the number of cards flipped over until the first ace appears and X2 be the number of cards flipped over until the second ace appears. What is the joint probability mass function of X1 and X2? What are the marginal distributions of X1 and X2?

A standard deck of 52 cards is thoroughly shuffled and laid face-down. You flip over the cards one by one. Let the random variable X1 be the number of cards flipped over until the first ace appears and X2 be the number of cards flipped over until the second ace appears. What is the joint probability mass function of X1 and X2? What are the marginal distributions of X1 and X2?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Calculate xpectation and variance of X, if the probability distribution of the random variable X is given by X 1 0.3 f - 0 0.1 1 0.1 2 3 0.3 0.2 shodm
Two balls are selected at random from an urn that contains three white balls and seven red balls. Let the random variable X denote the number of white balls drawn times the number of red balls drawn. Find the probability distribution. (Order your answers from smallest to largest x-value. Round your answers to four decimal places.)
You want to find the probability that people will return a shopping cart to the corral after loading the groceries in their vehicle. For a 4 hours period, you observe the number of people who returned their cart and the number who did not. A success in this case would be that the person returned their cart. Choose the best statistical tool to calculate this probability A. Use the Central Limit Theorem to find the probability that the sample mean exceeds a certain value B. Use the empirical rule to find the number of cars that bracket 68% of the data C. Calculate a confidence interval for the population mean D. Calculate the total number of successes divided by the total number of observations to find the observed probability
X is normally distributed with ?=14 and ?= 4. Find the probability that x is between 1 and 18.
Assume that the arrival rate of students entering a particular class late is 3 students. If I assume a normal distribution for this arrival rate, how big is my absolute error for the probability of 5 or fewer students arriving late?
Use Normal distribution table or otherwise to find the probability that Z > 2
Let X and Y be two independent random variables from exponential distribution with mean 3 and 4, respectively. Find P (6Y > X) Note: Please round your answer to 4 decimal places.
Suppose that you take a sample of size 40 from a population that is normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution? What if the population was not normally distributed, can the sampling distribution of x̄ be approximated by a normal probability distribution?
The random variable x represents the number of emails a student receives on a day. Assume it has a Poisson distribution with a mean of 14.3 emails. Find the probability that in a random day the student receives 3 emails. Round your answer to four decimal places.
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.4 and ß = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.74310 0.74310 0.12183 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 6032 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) hr
The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 5 students who fail per sem. d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period. e. Calculate the probability that there will be a failing student within the first semester. F. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester?