Question

An electronics retailer offers an optional protection plan for a mobile phone it sells. Customers can choose to buy the protection plan for

\[\$100\], and in case of an accident, the customer pays a
\[\$50\] deductible and the retailer will cover the rest of the cost of that repair. The typical cost to the retailer is
\[\$200\] per repair, and the plan covers a maximum of
\[3\] repairs.
Let
\[X\] be the number of repairs a randomly chosen customer uses under the protection plan, and let
\[F\] be the retailer's profit from one of these protection plans. Based on data from all of its customers, here are the probability distributions of
\[X\] and
\[F\]:

Answer 1

The mean of the probability mass of the random variable X is 0.14.

What is protection plan?

A protection plan is a financial arrangement or insurance policy designed to provide coverage and support against specific risks, damages, or losses. It aims to safeguard individuals or entities from unforeseen events.

An electronics retailer offers an optional protection plan for a mobile phone it sells. Customers can choose

to buy the protection plan.

Given

X: number of repairs a randomly chosen customer uses under the protection plan(random variable).

Probability mass table of discrete random variable X.

To find the expected value ,

Mean of X = Expected value of E(X).

E(X) = ΣxP(X=x)

= 0(0.90) + 1(0.07) + 2(0.02) + 3(0.01)

= 0 + 0.07 + 0.04 + 0.03

= 0.14

μₓ = 0.14

The mean of the probability mass of the random variable X is 0.14.

Complete question