Question

Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, with probabilities 0.3, 0.4, and 0.3, 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.

Required:
Determine the probability mass function of X. Round your answers to one decimal place (e.g. 98.7).

Answer 1

F(10) = P(x = 10) = 0.3

F(5) = P(x = 5) = 0.4

F(1) = P(x = 1) = 0.3

Explanation:

Given the following :

Probability estimates given:

Very successful = 0.3

Moderately successful = 0.4

Unsuccessful = 0.3

Yearly revenue (X) :

Very successful = $10 million

Moderately successful = $5 million

Unsuccessful = $1 million

The probability mass function of X:

f(x) = probability of each valie of x

When x = 10:

F(10) = P(x = 10) = 0.3

When x = 5:

F(5) = P(x = 5) = 0.4

When x = 1:

F(1) = P(x = 1) = 0.3