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2. A large but sparsely populated county has two small hospitals, one at the south end of the county and the other at the north end. The south hospital's emergency room has four beds, whereas the north hospital's emer- gency room has only three beds. Let X denote the num- ber of south beds occupied at a particular time on a given day, and let Y denote the number of north beds occupied at the same time on the same day. Suppose that these two rv's are independent; that the pmf of X puts probability masses .1, .2, .3, .2, and .2 on the x values 0, 1, 2, 3, and 4, respectively; and that the pmf of Y distributes probabilities .1, .3, .4, and .2 on the y values 0, 1, 2, and 3, respectively. a. Display the joint pmf of X and Y in a joint probabil- ity table. b. Compute P(X<1 and Y< 1) by adding probabilities from the joint pmf, and verify that this equals the produot

2. A large but sparsely populated county has two small hospitals, one at the south end of the county and the other at the north end. The south hospital's emergency room has four beds, whereas the north hospital's emer- gency room has only three beds. Let X denote the num- ber of south beds occupied at a particular time on a given day, and let Y denote the number of north beds occupied at the same time on the same day. Suppose that these two rv's are independent; that the pmf of X puts probability masses .1, .2, .3, .2, and .2 on the x values 0, 1, 2, 3, and 4, respectively; and that the pmf of Y distributes probabilities .1, .3, .4, and .2 on the y values 0, 1, 2, and 3, respectively. a. Display the joint pmf of X and Y in a joint probabil- ity table. b. Compute P(X<1 and Y< 1) by adding probabilities from the joint pmf, and verify that this equals the produot

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.8: Introduction To Cryptography (optional)
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I already know the solution for part C, so I would greatly appreciate help with parts A, B, and D. Thank you very much.

2. A large but sparsely populated county has two small hospitals, one at the south end of the county and the other at the north end. The south hospital's emergency room has four beds, whereas the north hospital's emer- gency room has only three beds. Let X denote the num- ber of south beds occupied at a particular time on a given day, and let Y denote the number of north beds occupied at the same time on the same day. Suppose that these two rv's are independent; that the pmf of X puts probability masses .1, .2, .3, .2, and .2 on the x values 0, 1, 2, 3, and 4, respectively; and that the pmf of Y distributes probabilities .1, .3, .4, and .2 on the y values 0, 1, 2, and 3, respectively. a. Display the joint pmf of X and Y in a joint probabil- ity table. b. Compute P(X<1 and Y< 1) by adding probabilities from the joint pmf, and verify that this equals the product of P(X s 1) and P(Y < 1). c. Express the event that the total number of beds occu- pied at the two hospitals combined is at most 1 in terms of X and Y, and then calculate this probability. d. What is the probability that at least one of the two hospitals has no beds occupied? 3. A certain
Transcribed Image Text:2. A large but sparsely populated county has two small hospitals, one at the south end of the county and the other at the north end. The south hospital's emergency room has four beds, whereas the north hospital's emer- gency room has only three beds. Let X denote the num- ber of south beds occupied at a particular time on a given day, and let Y denote the number of north beds occupied at the same time on the same day. Suppose that these two rv's are independent; that the pmf of X puts probability masses .1, .2, .3, .2, and .2 on the x values 0, 1, 2, 3, and 4, respectively; and that the pmf of Y distributes probabilities .1, .3, .4, and .2 on the y values 0, 1, 2, and 3, respectively. a. Display the joint pmf of X and Y in a joint probabil- ity table. b. Compute P(X<1 and Y< 1) by adding probabilities from the joint pmf, and verify that this equals the product of P(X s 1) and P(Y < 1). c. Express the event that the total number of beds occu- pied at the two hospitals combined is at most 1 in terms of X and Y, and then calculate this probability. d. What is the probability that at least one of the two hospitals has no beds occupied? 3. A certain
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