Discrete random variable

In summary, a random variable X takes integer values with equal probabilities. The expectation R for X is 50.5 and the variance Q^2 is given by 12Q^2=n^2-1. When n=100, R=50.5 and Q=28.87. The probability P(|X-50.5|>28.87) can be simplified to P(X\ge 80), which is equal to 1/100. This is because all the probabilities for X add up to 1, so any individual value has a probability of 1/100.
  • #1
thereddevils
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0

Homework Statement



A random variable X takes values 1,2,...,n with equal probabilities. Determine the expectation, R for X and show that the variance, Q^2 is given by 12Q^2=n^2-1. Hence, find
P(|X-R|>Q) in the case n=100

Homework Equations





The Attempt at a Solution



I can show that 12Q^2=n^2-1 but not the latter.

Substituting n=100, R=50.5 and Q=28.87

P(|X-50.5|>28.87)=P(X-50.5>28.87)+P(x-50.5<-28.87)

How can i continue from here?
 
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  • #2
What is P(X - 50.5 > 28.87)? You might start by figuring out in words just what this expression means. It's pretty simple to get the answer once you understand the expression.
 
  • #3
All values for x are of equal probability. There are 100 possible value. What is the probability that x takes a special value, like x=10?

ehild
 
  • #4
ehild said:
All values for x are of equal probability. There are 100 possible value. What is the probability that x takes a special value, like x=10?

ehild

If this is a discrete random variable, how can it take values which is not discrete ie with decimals?

To answer your question, all the probabilities add up to 1 so any value would have a probability of 1/100.

Am i correct?
 
  • #5
Yes, that is correct- if there are n possible outcomes and they are all equally likely, then the probability of anyone outcome is 1/n. Since there are only integer outcomes, "X- 50.5> 28.87", which is the same as "X> 79.37" is really "[itex]X\ge 80[/itex]".
 
  • #6
thereddevils said:
If this is a discrete random variable, how can it take values which is not discrete ie with decimals?

X takes integer values. What is the probability that x takes the value 1 or 2 or 3... up to 21 or 80 or 81 ... up to 100?

ehild
 
  • #7
Thanks all for helping me out.
 

What is a discrete random variable?

A discrete random variable is a type of variable in statistics that can take on a countable number of values, rather than a continuous range of values. This means that the possible outcomes of the variable are finite or countably infinite.

How is a discrete random variable different from a continuous random variable?

A discrete random variable can only take on specific values, while a continuous random variable can take on any value within a given range. Additionally, the probability of obtaining a specific value for a discrete random variable is always a finite number, while for a continuous random variable, the probability of obtaining a specific value is infinitesimal.

What is a probability distribution for a discrete random variable?

A probability distribution for a discrete random variable is a table, graph, or mathematical formula that shows the possible outcomes of the variable and their corresponding probabilities. It represents the likelihood of obtaining each possible outcome of the variable.

How is the mean of a discrete random variable calculated?

The mean of a discrete random variable is calculated by multiplying each possible outcome by its corresponding probability, and then summing up all of these values. This is also known as the expected value of the variable.

What are some examples of discrete random variables?

Examples of discrete random variables include the number of children in a family, the number of heads obtained when flipping a coin, and the number of cars in a parking lot. Other examples can include the number of students in a class, the number of goals scored in a soccer game, and the number of red M&Ms in a bag of candy.

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