Recent content by jashua

Why do you need to obtain a binomial distribution? The question does not require this.

Can you give your reasoning? May I ask what your computational result is?

Your answer finds P(K>=3), but OP asks for P(K=3).

I think you mean "...we will have 3 crowns...". You will have 3 crowns after flipping a coin 6 times in (6 choose 3) different ways, right? And you get a crown with probability p = 0.3, which implies that you will not have a crown with probability q = 1-p = 0.7. Suppose one of the experiments...

Think that you place 9 women around the circular table. As the question requires the number of circular permutations, there are (9-1)! ways to place 9 women. Now there are 9 spaces to place 6 men such that none of these 6 men sit next to each other. Then, just find the number of ways to place 6...

It seems z = 1 + ik, where k is an integer. It is also interesting to notice that f(z) is periodic with 1, as mfb has said. Then the relation between f(z) and f(z+i) must hold for z = r + ik, where both r and k are integers.

As f(x)=f(x+3)f(x-3)=f(x+3)f(x)f(x-6), we have f(x+3)f(x-6)=1 (ignoring that f(x)=0). Then, f(x)f(x-9)=1. Similarly, we find that f(x)f(x+9)=1. As a result, f(x+9)=f(x-9), and so, f(x)=f(x+18). Thus, n=18.

There are 17 possible ways you choose 2 balls with replacement such that Z=max(X,Y)=9. The number of all possible ways you choose 2 balls with replacement is 100. Now you should be able to find the answer.

As you have written, let a\begin{pmatrix} 1 & 2\\ 1 & 0 \end{pmatrix}+b \begin{pmatrix} 3 & 7\\ 0 & 0 \end{pmatrix}+c \begin{pmatrix} 2 & 6\\ \alpha & 0 \end{pmatrix}= \begin{pmatrix} 0 & 0\\ 0 & 0 \end{pmatrix} Then, \begin{pmatrix} a+3b+2c & 2a+7b+6c\\ a+c\alpha & 0 \end{pmatrix} =...

Ray, thank you very much for your detailed answer.

I think we can formulize your solution as follows: Let n(A) : # of passwords without any number, n(B): # of passwords without any letter, n(C): # of passwords without any symbol, n(S): # of passwords in the full set. Then, we calculate n(S)-n(A\cup B\cup C), where n(A\cup B\cup...

The lower limit does not become 0 if you expand the expression. I mean the linear substitution changes the lower limit.

A signal has its Fourier transform if and only if its ROC of Laplace transform contains the imaginary axis s=jw. The statement that you give is valid only for the right-hand sided signals for which the ROC is the right hand side of the poles. Fourier transform and Laplace transfrom (whether...

If that is the final version of the integral then it is enough to say that the equality holds.

Your assumtion is not enough to show one of the relations is true. It seems you need to show that the integrand is periodic with T/(1+\alpha).