According to wikipedia lack of memory property applies to geometric and exponential distributions. I was trying to apply it to binomial distribution. Am I modelling my question correctly?
So imagine a fair coin toss and X the random variable for number of heads. Assume number of trials to be 7.
Question: what is the probability that in seven tosses of a fair coin first 2 are tails and in remaining 5 tosses you get three heads?
So should the answer be: 0.5 x 0.5 x (5c3 x 0.5^3 x 0.5^2)
And how is it different from the following question: Tom tosses a coin twice and gets 2 tails. What is the probability that he will get three heads in remaining 5 tosses?
If the lack of memory property came into picture second time then is it correct to say that lack of memory property applies to binomial distribution too.
to the second question: The first two tosses must not be considered because the results already confirmed.
greetings,
calculus