1. [PDF, Mean (or Expected Value), and Standard Deviation] People visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Video To Go is given in the following table. There is a five-video limit per customer at this store, so nobody ever rents more than five DVDS. P(X) 0.03 1 0.5 2 0.24 3 4 0.07 5 0.04 (a) Describe the random variable X in words. (b) Find the probability that a customer rents three DVDS. (c) Find the probability that a customer rents at least four DVDS. (d) Find the probability that a customer rents at most two DVDS. Another shop, Entertainment Headquarters, rents DVDS and video games. The probability distribution for DVD rentals per customer at this shop is given as follows. They also have a five-DVD limit per customer. P(X) 0.35 1 0.25 2 0.2 3 0.1 4 0.05 5 0.05 (e) At which store is the expected number of DVDS rented per customer higher?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
answers to part 1 (a to e)
![1. [PDF, Mean (or Expected Value), and Standard Deviation] People visiting video rental stores often rent more than one
DVD at a time. The probability distribution for DVD rentals per customer at Video To Go is given in the following table. There
is a five-video limit per customer at this store, so nobody ever rents more than five DVDS.
P(X)
0.03
1
0.5
2
0.24
3
4
0.07
5
0.04
(a) Describe the random variable X in words.
(b) Find the probability that a customer rents three DVDS.
(c) Find the probability that a customer rents at least four DVDS.
(d) Find the probability that a customer rents at most two DVDS.
Another shop, Entertainment Headquarters, rents DVDS and video games. The probability distribution for DVD rentals per customer at
this shop is given as follows. They also have a five-DVD limit per customer.
P(X)
0.35
1
0.25
2
0.2
3
0.1
4
0.05
5
0.05
(e) At which store is the expected number of DVDS rented per customer higher?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2ccd316-53b0-4aef-b22f-fa386f44d50a%2F00628fa1-d863-4c6c-9ab1-056accdc1954%2F4622bn9.png&w=3840&q=75)
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