An electric circuit contains 5 components. It is known that 1 of the components is faulty. To determine the faulty component,all 5 components are tested one by one until the faulty component is found. The random variable X represents the number of tests required to determine the faulty component. If all 5 components have an equal chance of being faulty,find the expectation and variance of X.
Thanks for your help.
I've tried solving the question again.
P(X=1)=1/5
P(X=2)=(1/5)(4/5)
P(X=3)=(1/5)(4/5)^2
P(X=4)=(1/5)(4/5)^3
P(X=5)=(1/5)(4/5)^4
E(X)= (1)(1/5)+(2)(1/5)(4/5)+(3)(1/5)(4/5)^2+(4)(1/5)(4/5)^3+(5)(1/5)(4/5)^4
=1.7232
Is this correct???
I made a mistake earlier. It's not geometric.
The probability that you need 1 test (that is, you get the faulty component in the first selection) is 1/5.
The probability that you need 2 tests (that is, you get the faulty component in the second selection) is (4/5)(1/4) = 1/5.
The probability that you need 3 tests (that is, you get the faulty component in the third selection) is (4/5)(3/4)(1/3) = 1/5.
etc.
So E(number of tests) = 1(1/5) + 2(1/5) + 3(1/5) + .... + 5(1/5) = 15/5 = 3.
Get the variance in a similar way.