Question

An insurance for an appliance costs $52 and will pay $520 if the insured item breaks. The insurance company estimates that 2% of the insured items will break.

Let XX be the random variable that assigns to each outcome (item breaks, item does not break) the profit for the company. A negative value is a loss.

(a) Complete the table below.

X	52	-520
p(x)	Answer	0.02

(b) Calculate the expected profit for the company for each insurance policy. In other words, find the expected value of X.X. μX=μX=

(c) Find the variance of X.X. Var(X)=Var(X)=

(d) Find the standard deviation of X.X. σX=σX=

Answer 1

(a) as the sum of probability should be equal to 1 therefore Answer is

X	52	-520
p(x)	0.08	0.02

(b) the expected profit

(c) variance of

(d) standard deviation of XX is the square root of variance. Therefore,