Maximum Likelihood estimator for family of binomial distributions For the below example, I am considering Heads as a success and Tails as a failure, when I toss a coin.
(Ex: The first row in the the below tables says, when I tossed the coin 10 times I got 3 Successes and the probability of success is 0.3).
Binomial Distribution Example

Now, considering the fact that the Probability of successes might change by increase in trials, I know the maximum likelihood estimator of binomial distribution is Number of Successes/ Total Number of Trials. I feel calculating the MLE for this kind of data is not that straightforward, COuld someone tell me if I am missing something?
P.S: This is a research based question. Any help would be appreciated. Thanks in advance.
 A: Since per clarification comment, we are tossing the same coin, then in each single Bernoulli trial the probability is the same, $p$, it is not affected by number of trials (assuming also an unbiased way of tossing). If moreover we can assume that all Bernoulli trials are independent, and that each sub-sample consists of different tosses (i.e. the $n=20$ sample does not contain the $10$ tosses of the $n=10$ sample), then, viewed together, we have an independent but non-identically distributed sample of realizations from $10$ Binomials that have the same unknown probability parameter, but different "number of trials" parameters (although known and deterministic), $S_i(n_i,p), i=1,2,3,...,10$, corresponding to  $n$-parameters $10,20,30,...,100$.  
Then the joint likelihood of this sample is (ignoring constants that do not include the unknown parameter)
$$L \propto \prod_{i=1}^{10}p^{k_i}(1-p)^{n_i-k_i} = p^{\sum k_i}(1-p)^{\sum (n_i-k_i)}$$
where $k_i$'s are the obtained number of successes
So the log-likelihood is
$$\ln L = \left(\sum_{i=1}^{10}k_i\right)\ln p + \left(\sum_{i=1}^{10}(n_i-k_i)\right)\ln (1-p)$$
You should get
$$\hat p = \frac {\sum_{i=1}^{10}k_i}{\sum_{i=1}^{10}n_i}$$
as should be expected, since you pooled i.i.d. Bernoulli draws, and so the estimator treated them as $\sum_{i=1}^{10}n_i$ draws from a Bernoulli $(p)$ RV in which we had $\sum_{i=1}^{10}k_i$ successes.
