1. Toss a fair coin once. Let X be the number of tails that occur. Find the probabilitymass function of X.2. Draw a random card from a standard deck of cards. Let x denote the suits of thatrandom card. Find the probability mass function of X.3. Toss a pair of dice. Let X be the maximum value of the two tosses. For example, ifone die shows 3 while the other die shows 5, then X 5. Find the probability massfunction of X and graph it using the histogram.4 A certain business company has five activetelephone lines. Let x denote the number oflines in use at a particular time of day. Theprobability mass function of X is given below.230.050.150.280.340.160.02Find the probability that at least 3 telephone lines are in use at a particular time ofday.

Given that Tossed a fair coins one then the total outcomes is 2 Sample space=S=(H,T) X=the number…

Answered: 1. Toss a fair coin once. Let X be the…

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...

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Let X be the number of tails in three flips of a fair coin. Let Y be the outcome of a roll of a fair six-sided die. Assume X and Y are independent. Give the joint probability mass function of X,Y. Be precise about the values for which the joint probability mass function is defined.
This problem involves drawing three cards from a deck of cards. Assume that the deck contains 3 aces, 5 other face cards, and 15 non-face cards and that you randomly draw 3 cards. A random variable Z is defined to be 5 times the number of aces plus 4 times the number of other face cards drawn. 1. How many different values are possible for the random variable Z? 2. Fill in the table below to complete the probability density function. Be certain to list the values of Z in ascending order.
Each of three balls are randomly placed into one of three bowls. Let X be the number of empty bowls. i. Define the sample space S. i. Give all possible values of X. i. Use the table to express the probability mass function P(X = x).
Answer the last three
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
a box contains 6 balls, 4 of which are red. I randomly select 3 balls from the box. Find the probability mass function of getting 2 red balls?
2. Suppose a coin having probability 0.7 of coming up heads is tossed three times. Let X denote thenumber of heads that appear in the three tosses.(a) List down the possible values of X.(b) Determine the probability mass function of X.

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1. Toss a fair coin once. Let X be the number of tails that occur. Find the probability mass function of X. the suits of th