Discrete probability distributions

In summary, a discrete probability distribution is a statistical distribution that shows the probability of a discrete random variable taking on a specific value. It differs from a continuous probability distribution in that it deals with discrete random variables, and some common examples include the binomial, Poisson, and geometric distributions. The probability of a specific outcome in a discrete probability distribution is determined by dividing the number of favorable outcomes by the total number of possible outcomes, and these distributions are important in scientific research for making predictions and informing decision-making processes.
  • #1
somecelxis
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Homework Statement


Here's the question:
Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 .
Detrmine value of E(X^2)
the ans is 23/3 . but i ended up getting 3 . why i am wrong?


Homework Equations





The Attempt at a Solution

 

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  • #2
somecelxis said:

Homework Statement


Here's the question:
Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 .
Detrmine value of E(X^2)
the ans is 23/3 . but i ended up getting 3 . why i am wrong?


Homework Equations





The Attempt at a Solution


##\text{Var}(X-2) = \text{Var}(X)## because ##\text{Var}(\cdot)## is unaffected by a non-random shift. Also: ##\text{Var}(X) = E(X^2) - (EX)^2##.
 
  • #3
somecelxis said:

Homework Statement


Here's the question:
Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 .
Detrmine value of E(X^2)
the ans is 23/3 . but i ended up getting 3 . why i am wrong?

You made a mistake when expanding (x-2)2.

ehild
 
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Likes 1 person
  • #4
ehild said:
somecelxis said:

Homework Statement


Here's the question:
Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 .
Detrmine value of E(X^2)
the ans is 23/3 . but i ended up getting 3 . why i am wrong?

You made a mistake when expanding (x-2)2.

ehild

I guess I would have caught that if the OP had typed out his work, but since I never read attached thumbnails I missed it.
 

1. What is a discrete probability distribution?

A discrete probability distribution is a statistical distribution that shows the probability of a discrete random variable taking on a specific value. It is used to represent the probability of different outcomes in a discrete set of events, such as rolling a dice or flipping a coin.

2. How is a discrete probability distribution different from a continuous probability distribution?

A discrete probability distribution deals with discrete random variables, which can only take on certain values, while a continuous probability distribution deals with continuous random variables, which can take on any value within a given range. For example, the number of heads when flipping a coin is a discrete random variable, while the height of a person is a continuous random variable.

3. What are some common examples of discrete probability distributions?

Some common examples of discrete probability distributions include the binomial distribution, the Poisson distribution, and the geometric distribution. These distributions are often used to model real-world phenomena, such as the number of successes in a series of independent trials or the number of customers arriving at a store in a given time period.

4. How is the probability of a specific outcome determined in a discrete probability distribution?

In a discrete probability distribution, the probability of a specific outcome is determined by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the probability mass function, which assigns a probability to each possible value of the random variable.

5. What is the importance of discrete probability distributions in scientific research?

Discrete probability distributions are essential in scientific research as they allow researchers to model and analyze the likelihood of different outcomes in discrete events. This enables them to make predictions and draw conclusions based on data, helping to inform decision-making processes and advance scientific understanding.

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