- #1
Gunmo said:Could you have a look new attachment please.
Thank you for finding error in attachment
Gunmo said:Yes, this is actually about probability.
Gunmo said:Not sure yet, this eventually
Sigma ( x * k^x) 0<k<1 x = 1, 2, 3, 4, 5....n=infinite
x is approach infinite,
k^x approach 0.
The answer is, 1/k.
StoneTemplePython said:## E[X] = 1 + (1-p)E[X]##
Then solve for ##E[X]##
.
Charles Link said:@PeroK : Please read my post #10. I don't think it is binomial. As @StoneTemplePython says, here the OP's problem is to calculate the expected number of coin flips until heads occurs, given that heads occurs with probability p. (The OP's formula is not calculating the probability of ## k ## successes in ## n ## trials, nor the mean number of successes of a binomial distribution.) ## \\ ## Note: The "trick" that is most readily employed in solving this one is essentially the same one (taking a derivative w.r.t. ## p ##) in solving the mean ## k ## for a binomial, but this one is not the binomial distribution.
PeroK said:If this isn't a binomial distribution I don't know what is. True, you are calculating the mean time to get the first occurrence, but it's clearly a binomial.
A geometric progression is a sequence of numbers where each term is found by multiplying the previous term by a fixed number. For example, the sequence 2, 4, 8, 16, 32 is a geometric progression with a common ratio of 2.
To prove that a sequence is a geometric progression, you need to show that each term is obtained by multiplying the previous term by a fixed number. You can also use the formula for the nth term of a geometric progression, which is given by a * r^(n-1), where a is the first term and r is the common ratio.
The formula for the sum of a geometric progression is given by S = a * (1 - r^n)/(1 - r), where a is the first term, r is the common ratio, and n is the number of terms. This formula can be derived using the formula for the sum of a finite geometric series.
Geometric progressions can be used to model many real-life situations, such as population growth, compound interest, and radioactive decay. They can also be used in various fields of science, such as physics and biology, to describe and predict patterns and relationships.
Yes, as a scientist, I have a strong understanding of geometric progressions and their properties. I would be happy to assist you with any specific proof that you may need help with. Please provide more details about the proof and I will do my best to guide you through it.