CMOCO LO NALEDI N. SE TLALEKAOS 102100532 NALEDI SETCALFEGO 20 7 Question Al SECTION A (ANSWER ALL QUESTIONS IN THIS SECTION) (a) Let A and B be events with P (4) 0.75 and P(B)-0.6 and P(A)=0.15 (i) Find P(AUB). (ii) Find P(A|B). (iii) Are events A and B independent? Justify your answer. (b) Suppose X is a random variable from the probability mass function 3 ,x=0,1,2 f(x)=3k (i) Find the value of k. (ii) Evaluate P(10.96. (b) The probability distribution of the discrete random variable X is 6-x -Q60*. f(x)= (i) Find P(42) x=0,1,2,3,4,5,6 (ii) Find the mean and variance of random variable Y=2x+1. Question B2 [3] [3] [4] [3] [3] [4+5] (a) The lifespan, in hours, of a fuse used in a mechanical operation has a distribution function G(x)=1-e, x>0 (i) Find the probability density function. Find the probability that the fuse will fail (ii) between 1 hours and 4 hours of usage. [6] (iii) less than 0.01 hour of usage. (b) Suppose X1, X2, X3 is a random sample of size 3, from normal distribution with mean 0 and variance 5. (i) Find and describe the probability distribution of W = ½-(x²+x²+X²) (ii) Evaluate the probability P(0.185
CMOCO LO NALEDI N. SE TLALEKAOS 102100532 NALEDI SETCALFEGO 20 7 Question Al SECTION A (ANSWER ALL QUESTIONS IN THIS SECTION) (a) Let A and B be events with P (4) 0.75 and P(B)-0.6 and P(A)=0.15 (i) Find P(AUB). (ii) Find P(A|B). (iii) Are events A and B independent? Justify your answer. (b) Suppose X is a random variable from the probability mass function 3 ,x=0,1,2 f(x)=3k (i) Find the value of k. (ii) Evaluate P(10.96. (b) The probability distribution of the discrete random variable X is 6-x -Q60*. f(x)= (i) Find P(42) x=0,1,2,3,4,5,6 (ii) Find the mean and variance of random variable Y=2x+1. Question B2 [3] [3] [4] [3] [3] [4+5] (a) The lifespan, in hours, of a fuse used in a mechanical operation has a distribution function G(x)=1-e, x>0 (i) Find the probability density function. Find the probability that the fuse will fail (ii) between 1 hours and 4 hours of usage. [6] (iii) less than 0.01 hour of usage. (b) Suppose X1, X2, X3 is a random sample of size 3, from normal distribution with mean 0 and variance 5. (i) Find and describe the probability distribution of W = ½-(x²+x²+X²) (ii) Evaluate the probability P(0.185
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
Related questions
Question
![CMOCO LO NALEDI N. SE TLALEKAOS
102100532
NALEDI SETCALFEGO
20
7
Question Al
SECTION A
(ANSWER ALL QUESTIONS IN THIS SECTION)
(a) Let A and B be events with P (4) 0.75 and P(B)-0.6 and P(A)=0.15
(i) Find P(AUB).
(ii) Find P(A|B).
(iii) Are events A and B independent? Justify your answer.
(b) Suppose X is a random variable from the probability mass function
3
,x=0,1,2
f(x)=3k
(i) Find the value of k.
(ii) Evaluate P(1<x<4).
Find the mean and variance of Y=5-3X.
Question A2
(a) A continuous random variable X has probability density function
g(x)=m (1+x),-2<x<3
[2]
[3]
[3]
[3]
[3]
[4+5]
(i) Find the value of m.
[3]
(ii) Find the distribution function, G(x) = P(X ≤x).
[4]
(iii) Evaluate P(2<X<5).
[3]
(b) A product output is known to be 0.5% defective. In a random sample of 600 components,
use Poisson distribution determine how many will have two or more defectives?
V(c) Given a random sample of size 24 from a normal population, find k such that:
[5]
P(k<T<2.807)=0.095, where T has t23)-distribution.
[3]
(d) Samples of 10A fuses have a mean fusing current of 9.9A and a standard deviation of
1.2A. Determine the probability of a fuse blowing with a current between 8.1A and 11.8A.
2
0.379473319
-1.5
[5]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2006393e-c97e-4081-8173-0190425f3dd9%2Fae31373a-c690-456c-ba4c-a3154e8e8221%2Fza2dd4b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:CMOCO LO NALEDI N. SE TLALEKAOS
102100532
NALEDI SETCALFEGO
20
7
Question Al
SECTION A
(ANSWER ALL QUESTIONS IN THIS SECTION)
(a) Let A and B be events with P (4) 0.75 and P(B)-0.6 and P(A)=0.15
(i) Find P(AUB).
(ii) Find P(A|B).
(iii) Are events A and B independent? Justify your answer.
(b) Suppose X is a random variable from the probability mass function
3
,x=0,1,2
f(x)=3k
(i) Find the value of k.
(ii) Evaluate P(1<x<4).
Find the mean and variance of Y=5-3X.
Question A2
(a) A continuous random variable X has probability density function
g(x)=m (1+x),-2<x<3
[2]
[3]
[3]
[3]
[3]
[4+5]
(i) Find the value of m.
[3]
(ii) Find the distribution function, G(x) = P(X ≤x).
[4]
(iii) Evaluate P(2<X<5).
[3]
(b) A product output is known to be 0.5% defective. In a random sample of 600 components,
use Poisson distribution determine how many will have two or more defectives?
V(c) Given a random sample of size 24 from a normal population, find k such that:
[5]
P(k<T<2.807)=0.095, where T has t23)-distribution.
[3]
(d) Samples of 10A fuses have a mean fusing current of 9.9A and a standard deviation of
1.2A. Determine the probability of a fuse blowing with a current between 8.1A and 11.8A.
2
0.379473319
-1.5
[5]
![OMOGOLO NALEDI N SETLALEKAOSI
*00532
NALEDI SETLALESGOS!
202100532
MAT 27 TEST
Question B1
SECTION B
(ANSWER ANY TWO QUESTIONS IN THIS SECTION)
6-3
(a) A random variable X has mean =8, variance σ 9 and an unknown probability
distribution. Use Chebyshev's theorem to find the bounds of:
) P(X-826).
(i) P(-4<X<20).
(iii) Find c such that P(X-8<4c)>0.96.
(b) The probability distribution of the discrete random variable X is
6-x
-Q60*.
f(x)=
(i) Find P(4<X<8)
(ii) Find P(X>2)
x=0,1,2,3,4,5,6
(ii) Find the mean and variance of random variable Y=2x+1.
Question B2
[3]
[3]
[4]
[3]
[3]
[4+5]
(a) The lifespan, in hours, of a fuse used in a mechanical operation has a distribution function
G(x)=1-e, x>0
(i) Find the probability density function.
Find the probability that the fuse will fail
(ii) between 1 hours and 4 hours of usage.
[6]
(iii) less than 0.01 hour of usage.
(b) Suppose X1, X2, X3 is a random sample of size 3, from normal distribution with
mean 0 and variance 5.
(i) Find and describe the probability distribution of W = ½-(x²+x²+X²)
(ii) Evaluate the probability P(0.185<W<9.837)
8-36128-3=-43
8+4=3k
LB
[4]
[3]
[8]
[4]
P(X-MJ << x+6)=½•
Pla-(MFO)<-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2006393e-c97e-4081-8173-0190425f3dd9%2Fae31373a-c690-456c-ba4c-a3154e8e8221%2Fs9kgux_processed.jpeg&w=3840&q=75)
Transcribed Image Text:OMOGOLO NALEDI N SETLALEKAOSI
*00532
NALEDI SETLALESGOS!
202100532
MAT 27 TEST
Question B1
SECTION B
(ANSWER ANY TWO QUESTIONS IN THIS SECTION)
6-3
(a) A random variable X has mean =8, variance σ 9 and an unknown probability
distribution. Use Chebyshev's theorem to find the bounds of:
) P(X-826).
(i) P(-4<X<20).
(iii) Find c such that P(X-8<4c)>0.96.
(b) The probability distribution of the discrete random variable X is
6-x
-Q60*.
f(x)=
(i) Find P(4<X<8)
(ii) Find P(X>2)
x=0,1,2,3,4,5,6
(ii) Find the mean and variance of random variable Y=2x+1.
Question B2
[3]
[3]
[4]
[3]
[3]
[4+5]
(a) The lifespan, in hours, of a fuse used in a mechanical operation has a distribution function
G(x)=1-e, x>0
(i) Find the probability density function.
Find the probability that the fuse will fail
(ii) between 1 hours and 4 hours of usage.
[6]
(iii) less than 0.01 hour of usage.
(b) Suppose X1, X2, X3 is a random sample of size 3, from normal distribution with
mean 0 and variance 5.
(i) Find and describe the probability distribution of W = ½-(x²+x²+X²)
(ii) Evaluate the probability P(0.185<W<9.837)
8-36128-3=-43
8+4=3k
LB
[4]
[3]
[8]
[4]
P(X-MJ << x+6)=½•
Pla-(MFO)<-
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