The marketing director for a small manufacturer of personal computers

dictetzqh

dictetzqh

Answered question

2021-11-17

The marketing director for a small manufacturer of personal computers (PCs) believes that the discrete probability distribution shown in the following table characterizes the number, y, of new PDs the firm will lease next year.
Leased Personal Computers
y78910111213P(y)0.100.100.150.200.200.150.10
1. Is this a valid probability distribution?
2. What is the probability that exactly 9 PCs will be leased?
3. What is the probability that fewer than 12 PCs will be leased?

Answer & Explanation

Troy Lesure

Troy Lesure

Beginner2021-11-18Added 26 answers

1. Consider a random variable y with probability distribution of p(y). Now, p(y) is said to be a valid probability distribution if p(y)0 and p(y)=1.
From the given probability distribution table, it is obtained that, p(y)>0.
Moreover, p(y)=0.10+0.10+0.15+0.20+0.20+0.15+0.10=1.
Hence, it is a valid probability distribution.
2. Here, the random variable y defines the number of new PCs the firm will lease next year.
Thus, the probability that exactly 9 PCs will be leased is, P(y=9)=0.15.
3. The probability that fewer than 12 PCs will be leased is, P(y<12)=P(y=7)+P(y=8)+P(y=9)+P(y=10)+P(y=11)=0.10+0.10+0.15+0.20+0.20=0.75.

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