Marketing estimates that a new instrument for the analysis of soil samples will

Question

Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, with probabilities 0.4, 0.5, and 0.1, respectively. The yearly revenues associated with a very successful, moderately, or unsuccessful product are $10 million, $5 million, and $1 million, respectively. Let the random variable X denote the yearly revenue of the product. Determine the probability mass function of X. Round your answers to one decimal place (e.g. 98.7).

Probability Mass Function of X

f(x) P(x-$10 million) = P( X=$5 million)- P(X= $1 million)

Explanation / Answer

As the revenue will be $10 million in very successful condition for which the probability is 0.4, therefore P(X = $10 million) = 0.4

Similarly, there is a revenue projected to be moderately successful with a probability of 0.5 when the revenue would be $5 million. Therefore P(X = $5 million ) 0.5

And lastly in a similar manner for an unseccessful condition we get: P(X = $1 million ) = 0.1

Therefore we get the probability mass function for X as:

X f(x) P(X = $10 million ) 0.4 P(X = $5 million ) 0.5 P(X = $1 million ) 0.1

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