Question

Probability that Alice will accidentally drop her phone to ground is p. She will not be careful after any no.of unfortunate events. Let X be the random variable that equals to the no.of times Alice drops her phone. Write a program to calculate the expectation value, E(X).

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

Explanation:

X is the random variable that equals the number of times she drops the phone.

Expected value is the mean over all the outcomes. Here the number of times is not given so it is infinity.

E(X) = sigma vi over infinite(vi*P(vi))

= 1*P(1)+2*P(2)+3*P(3)+......

=1*p+2*p^2+3*p^3+.....

=p(1+2p+3p^2+....)

=p((1+p+p^2+p^3+.....) + (p+p^2+p^3+.....) + (p^2+p^3+p^4+....) + (......) + (......) + ............)

=p((1/(1-p)) + (p/(1-p)) + (p^2/(1-p)) + ...............)

=p( (1+p+p^2+p^3+.........) / (1-p))

=p((1/(1-p) * (1/(1-p))

=p/(1-p)^2