An electronics firm decided to market four different software packages for its p

Question

An electronics firm decided to market four different software packages for its personal computers in the market. The marketing analyst gives each of four packages a 50% chance of success. The outcomes for each of the software packages are independent.

What is the probability of having no success in the market out of those four software packages?

Construct the probability table showing the probabilities of all possible cases (in terms of the number of successful software packages) from marketing efforts with those four software packages above in the market.

How many software packages do we expect to be successful in the market on average when all those four packages are introduced in the market? In other words, what is the expected value of the number of successful packages out of those four software packages in the market? What is the interpretation of this value?

What are the variance and the standard deviation for the above marketing experiment?

Explanation / Answer

This is binomial distribution with n=4 and p=0.5

As we know P(x)=ncxp^x(1-p)^n-x

P(x=0)= 0.0625

P(x=1)=0.25

P(x=2)= 0.375

P(x=3)=0.25

P(x=4)= 0.0625

Mean=np=0.5*4=2

Variance=np(1-p)=1

Sd=sqrt(1)=1

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