Question

The usable lifetime of a particular electronic component is known to follow an exponential distribution with a mean of 6.6 years. Let X = the usable lifetime of a randomly selected component.

(a) The proportion of these components that have a usable lifetime between 5.9 and 8.1 years is   .

(b) The probability that a randomly selected component will have a usable life more than 7.5 years is  .

(c) The variance of X is

Answer 1

here parameter β =6.6

a)

probability =

P(5.9<X<8.1)=

(1-exp(-8.1/6.6)-(1-exp(-5.9/6.6))=

0.1160

b)

probability =

P(X>7.5)=

1-P(X<7.5)=

1-(1-exp(-7.5/6.6))=

0.3210

c)

varaince =σ2=

β2 =

43.5600