Question

Q2- An electrician is interested in the life time density function of an electrical system consisting of 4 bulbs in a parallel layout when all the bulbs are working.

For the following situation, suggest the most appropriate statistical model for the variable interest. Hence,

i) define the variable, X.

ii) write the complete probability density function

iii) find its mean and variance. all in their commonly used forms and symbols.

Answer 1

Let Xi be random variable of life time of i th electric bulb

pdf of Xi

= 0 otherwise

AS all bulbs life is independent and identical

X i are independent and identical random variables

For four bulbs life time

( note for better explanation i change random variable symbol X to Y)

Mean

as pdf of gamma distribution

# variance

as pdf of gamma distribution

Variance

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