1. The total hours spent by adults playing video games in their life time are measured in an experiment. (a) Define the sample space of the experiment (b) Define E1 where the hours spent is from 10o hours or more and E2 if 100 hours or less (c) Find E1 U E2 and E1 n E2 (d) Are the events mutually exclusive?

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1. The total hours spent by adults playing video games in their life time are
measured in an experiment. (a) Define the sample space of the experiment (b)
Define E1 where the hours spent is from 100 hours or more and E2 if 100
hours or less (c) Find E1 U E2 and E1 n E2 (d) Are the events mutually
exclusive?
2. The passing rate of the universities taking the Engineering Board exams in
the past are as follow, 45% graduated from elite universities; 40% graduated
from private universities, 50% graduated from public universities, and all
became successful engineers. The current passing rate on the other hand is as
follows; 39% graduated from elite universities; 35% graduated from private
universities, 55% graduated from public universities. Find (a)the probability
that the current board exam passers would became successful engineers. (b)
the probability that the current board passer will be successful and from a
public university. (c) the probability that the current board passer will be
successful and from an elite university.
3. Given the probability mass function and the cumulative distribution
function of X
1
P(X = 2) =
;
4
P(X = 5)
15
P(X = 1) =
P(X = 3)
P(X = 4) =
15
F(0) = 0
;x< 0
1
F(x)
F(1)
;1< x< 2
15
1
8
F(2) =
;2 <x < 3
0.8
F(X) =
23
F(3) = 45
;3 <x< 4
0.6
11
F(4) =
15
;4 < x< 5
0.4
F(5) = 1
;5 < x
0.2
Cumulative distribution function of x
Determine:
(a) P(X < 3)
(b) P(1 < X < 3)
(c) P(1 < X < 3)
(d) P(1 < X < 4)
(е) Р(X > 2)
Transcribed Image Text:1. The total hours spent by adults playing video games in their life time are measured in an experiment. (a) Define the sample space of the experiment (b) Define E1 where the hours spent is from 100 hours or more and E2 if 100 hours or less (c) Find E1 U E2 and E1 n E2 (d) Are the events mutually exclusive? 2. The passing rate of the universities taking the Engineering Board exams in the past are as follow, 45% graduated from elite universities; 40% graduated from private universities, 50% graduated from public universities, and all became successful engineers. The current passing rate on the other hand is as follows; 39% graduated from elite universities; 35% graduated from private universities, 55% graduated from public universities. Find (a)the probability that the current board exam passers would became successful engineers. (b) the probability that the current board passer will be successful and from a public university. (c) the probability that the current board passer will be successful and from an elite university. 3. Given the probability mass function and the cumulative distribution function of X 1 P(X = 2) = ; 4 P(X = 5) 15 P(X = 1) = P(X = 3) P(X = 4) = 15 F(0) = 0 ;x< 0 1 F(x) F(1) ;1< x< 2 15 1 8 F(2) = ;2 <x < 3 0.8 F(X) = 23 F(3) = 45 ;3 <x< 4 0.6 11 F(4) = 15 ;4 < x< 5 0.4 F(5) = 1 ;5 < x 0.2 Cumulative distribution function of x Determine: (a) P(X < 3) (b) P(1 < X < 3) (c) P(1 < X < 3) (d) P(1 < X < 4) (е) Р(X > 2)
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