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, 0.3, and 0.4, 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).

Answer 1

Answer:

(in tabular format)

x            1            5            10

p(x)     0.4        0.3          0.3

Step-by-step explanation:

probability mass function (PMF) gives us probabilities of possibilities of a random variable. It is usually shown in a tabular format with Random Variable (x) in one column and each associated probability [P(x)] in its respective column.

Here, our random variable is the yearly revenues of being "very successful", "moderately successful", and "unsuccessful".

So we can write [in probability notation]:

P(x=10) = 0.3

P(x=5) = 0.3

P(x=1) = 0.4

This, in tabular format would be the probability mass function (PMF).

x            1            5            10

p(x)       0.4        0.3         0.3