Recent content by sabbagh80

Could you please define what you mean by L_i and X_j? Sorry, but, I am confused by these two notations.

yes, you are right. I had considered it in my mind, but, I forgot to mention it. So, we can modify the set as A=\{l_1,l_2 \in \{0,1,...,N\}|l_1+2l_2=l, l_1+l_2\leq N \}

We can say, it is a kind of tri-nomial distribution with a constraint of p_1+p_2=k where 0<k<1. And Pr[k_1=l] is the summation of the above pmf over the constraint of l_1+2l_2=l. If you sum up over all the values of l, you can easily get unity, since it is the summation of a tri-nomial...

I had done it before. it is (\frac{k l_1}{l_1+l_2})^{l_1} (\frac{k l_2}{l_1+l_2})^{l_2}.but the problem is that each term of the summation is maximized in different values of the given interval as l_1, l_2 vary.

Hi, What is the maximum value of the given summation in terms of k, l and N ? max_{0\leq x \leq k} \sum_{(l_1,l_2)\in A} \frac{N!}{(N-l_1-l_2)!l_1!l_2!} x^{l_1}(k-x)^{l_2}(1-k)^{N-l_1-l_2} where A=\{(l_1,l_2)|l_1,l_2 \in \{0,1,2,...,N\} and l_1+2l_2=l\} and 0<k<1. Thanks a lot for your...

Even when we find the upper bound of the p_1^{l_1}p_2^{l_2} as (\frac{kl_1}{l_1+l_2})^{l_1}(\frac{kl_2}{l_1+l_2}) ^{l_2} with the constraint of p_1+p_2=k \leq 1, but the main problem has not solved. If I rephrase the main problem again, it is as follows; f=max_{0\leq x \leq k} \sum_{l_1,l_2 \in...

Are you agree with the given upper bound for l_1, l_2 \in N and k \leq 1? I have to find the upper bound "in terms of p_1 + p_2=k" not "for" p_1 + p_2=k Also, about the probability space, except p_1 + p_2, we also have p_0=1-p_1-p_2=1-k.

Dear SW VandeCarr, let me explain the problem in other view and also my answer. Let p_1, p_2 be any two probability values with the constraint p_1+p_2=k\leq 1 where k is constant. Also, suppose l_1, l_2 \in N are two fixed numbers. Then, by maximization, we have: p_1^{l_1}p_2^{l_2}\leq...

It is a cute joke! m is from 0 to n not to infinity. by the way, thanks for your participation.

If I reword the problem, find the supreme (or at least one good) functionf(.) which for it we have p_1^{l_1}p_2^{l_2}\leq f(p_1+p_2,l_1,l_2)

What is your meaning, I am confused!

Can everybody show me how could I do the above suggestion?

Hi, I have sent this question a couple of days ago, but it seems that its latex form had problem. So, I decide to send it again. I will thank If somebody help me solving this problem. Consider a random variable k_1 with the given pmf as: Pr[k_1=l]=\sum_{l_1+2l_2=l}...

Hi, I will thank If somebody help me solving this problem. Consider a random variable k_1 with the given pmf as: Pr[k_1=l]=\sum_{l_1+2l_2=l} \frac{N!}{(N-l_1-l_2)!l_1!l_2!}p_1^{l_1} p_2^{l_2} (1-(p_1+p_2))^{N-l_1-l_2} where l_1,l_2 \in [0,1,...,l] . but we don't have p_1 and...

[SIZE="4"]Hi, I will thank If somebody help me solving this problem. Consider a random variable k_1 with the given pmf as: Pr[k_1=l]=\sum_{l_1+2l_2=l} \frac{N!}{(N-l_1-l_2)!l_1!l_2!}p_1^{l_1} p_2^{l_2} (1-(p_1+p_2))^{N-l_1-l_2}where l_1,l_2 \in [0,1,...,l] . but we don't have p_1 and p_2...