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).
Accepted Solution
A:
Answer:(in tabular format)x 1 5 10p(x) 0.4 0.3 0.3Step-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) = 0.3P(x=5) = 0.3P(x=1) = 0.4This, in tabular format would be the probability mass function (PMF).x 1 5 10p(x) 0.4 0.3 0.3