Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful with probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful product is $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.

Question

Mathematics

Lady

14 February, 06:16

Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful with probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful product is $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.

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Harris · Answer 1

X (millions) 1 5 10

P (x) 0,1 0,6 0,3

Step-by-step explanation:

In this case, the probability mass function of X is the function that relates the money produced for the product with the probability of obtain this profit of the product.

The mass function will be:

X (millions) 1 5 10

P (x) 0,1 0,6 0,3

This is a probability mass function because the sum of the probabilities of each value is 1. 0.1+0.6+0.3=1