1) A serial system is comprised of 5 components connected in series. In order fo

Question

1) A serial system is comprised of 5 components connected in series. In order for the serial system to work, all five components must function correctly. Assume that each component fails to function independently of the other components. The probability with which each component fails is 0.01 (a) What is the probability that the whole system functions correctly? (b) What is the probability that at most 3 of the 5 components fail? (c) Let X denote the number of components that fail to function. Find the probability mass function of X. (d) Let Y be a Bernoulli random variable that is equal to 1 if at least 4 components function correctly. Find the probability mass function of Y

Explanation / Answer

Ans:

Probabilty that a component is working=1-0.01=0.99

a)P(system functions corerctly)=P(all components work)=0.995=0.951

b)P(x<=3)=BINOMDIST(3,5,0.01,TRUE)=1

c)Binomial distribution:

P(x=r)=5Cr*0.01r*0.995-r

where r=0,1,2,3,4,5

d)first find p

p=P(x>=4)=5C4*0.994*0.011+5C5*0.995*0.010

=0.0480+0.951

=0.999

or use excel function:

P(x>=4)=1-P(x<=3)=1-BINOMDIST(3,5,0.99,TRUE)=0.9990

So,parameter of bernoulli' distribution p=0.999

pmf of Y:

f(k,p)=p ; if k=1

=1-p; if k=0

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