What Is the Expected Value E(X|X>=6) for a Geometric Distribution with p=0.20?

In summary: The event that X = k and X >= 6 is when the coin lands heads on the first throw and it repeats. The event that X = k and X >= 6 is when the coin lands heads on the first throw and it repeats. The event that X = k and X >= 6 is when the coin lands heads on the first throw and it repeats.
  • #1
ParisSpart
129
0
the random value X takes values 1,2,3... and has the X has geometric distribution with p=0.20 (This means that X can be interpreted as the time the first crown to repeated throws a coin coin lands heads with probability p.) what is the expected value E(X/X>=6)=?

i use this type : E(X/X>=6)=sum(k*P(X=k/X>=6))
but how i can estimate this> how i will find P(X=k and X>=6)=? and P(X>=6)=? where k=1,2,3...
 
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  • #2
[tex]
P(X = k) = (1-p)^{k-1}p
[/tex]

You can easily find the value of [itex]P(X \ge 6)[/itex] by realising that [itex]P(X \ge 6)=1-P(X<6)[/itex], which is computationally simple to evaluate (or use the equation for the cumulative distribution function, which you can find with a quick Google search).

[itex]P(X=k \cap X \ge 6)[/itex] is quite simple if you consider particular values of k. What is its value if [itex]k<6[/itex]? What about when [itex]k \ge 6[/itex]?
 
  • #3
What does the condition X>=6 mean in words?
What can you say about expectation of the number of additional throws required?

If you understand it, you can see the answer immediately.
 
  • #4
i found the P(X>=6) but i can't find the P(X=k AND x>=6) i sum all them :sum from k=6 to inf of p*(1-p)^(k-1) bt its not correct...
 
  • #5
ParisSpart said:
i found the P(X>=6) but i can't find the P(X=k AND x>=6) i sum all them :sum from k=6 to inf of p*(1-p)^(k-1) bt its not correct...

For k < 6, what is the event {X = k and X >= 6}? (Never mind about probabilities for now; just answer my question about the event. For k = 6, what is the event {X = k and X >= 6}? For k > 6, what is the event {X = k and X >= 6}?

As I said, answer these questions first, then worry afterwards about probabilities.
 

FAQ: What Is the Expected Value E(X|X>=6) for a Geometric Distribution with p=0.20?

1. What is "expected value with condition"?

"Expected value with condition" is a statistical concept that calculates the average outcome of a random variable under specific conditions or constraints.

2. How is "expected value with condition" different from regular expected value?

The main difference is that regular expected value considers all possible outcomes of a random variable, while "expected value with condition" only considers a subset of those outcomes that meet a specific condition.

3. What types of conditions can be used in "expected value with condition" calculations?

Any condition that can be expressed mathematically can be used in "expected value with condition" calculations. This includes inequalities, equations, and logical statements.

4. How is "expected value with condition" used in real-world applications?

"Expected value with condition" is commonly used in decision-making and risk analysis scenarios. It can help determine the most favorable course of action under certain constraints or identify potential risks based on specific conditions.

5. Can "expected value with condition" be negative?

Yes, "expected value with condition" can be negative if the condition results in a negative outcome. For example, if the condition is that a coin must land on tails, the expected value with condition would be -0.5 (since the expected value of a coin flip is 0.5).

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