Question

1. A recruiter, Joey Falcon, interviews 6 students. Each student has a probability of 0.2 of receiving a recommendation from Joey Falcon (the result from each student is independent from the results of the other students). Let X be the number students who Joey Falcon recommends.

A second recruiter, Sophie Secaucus, interviews 4 students (different from the above 6 students). Each student has a probability of 0.3 of receiving a recommendation from Sophie Secaucus (the result from each student is independent from the results of the other students. Let Y be the number of students who Sophie Secaucus recommends.

1. Find the joint pmf for X,Y (assume X and Y are independent).
2. Find p(X<3, Y<2)
3. Find p(X+Y<5)

Answer 1

ANSWER::

Given Data

X is the number of students that Joey Falcon recommends out of 6 each with probability 0.2 independent of each other , Hence ,

x = 0,1,2,---,6

Y is the number of students that Sophie Secaucus recommends out of 6 each with probability 0.3 independent of each other , hence,

y = 0,1,2,---,6

a) Find the joint pmf for X,Y (assume X and Y are independent)

Assuming X and Y are independent , joint pmf of X and Y is:

x,y = 0,1,2,----,6

b)  Find p(X<3, Y<2)

  

c) Find p(X+Y<5)

Following re the possible combinations of X and Y which satisfies X+Y<5 , with corresponding probabilities :

x	y	P(X=x,Y=y)
0	0	0.0308
0	1	0.0793
0	2	0.0850
0	3	0.0486
0	4	0.0156
1	0	0.0463
1	1	0.1190
1	2	0.1275
1	3	0.0728
2	0	0.0289
2	1	0.0743
2	2	0.0797
3	0	0.0096
3	1	0.0248
4	0	0.0018
	sum	0.8439

Hence ,

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