Thank you for your insistent reply.
As you suggested,
P(X=x \cap X+Y=m)=P(X=x \cap Y=m-x)= \frac{\lambda_1^x}{x!}e^{-\lambda_1} *\frac{\lambda_2^{m-x}}{(m-x)!} e^{-\lambda_2}=\lambda_2^m e^{-\lambda_1-\lambda_2} (\frac{\lambda_1}{\lambda_2})^x \frac{1}{m!} {m \choose x}
P(X+Y=m) =...
Homework Statement
If random variables X and Y are independent and both belong to Possion distribution of parameters \lambda_1 and \lambda_2 , then what is the conditional distribution of X when the condition X + Y = m is given?
Homework Equations
Possion distribution of...
Ray is professional.
Indeed, I should use some notation to explicitly describe the answer.
You have given the correct answer, it should be P(F|U) = \frac{P(F \cap U)}{P(U)} =
\frac{\sum_{i=1}^3 P(F \cap U | B_i) P(B_i)}{\sum_{i=1}^3 P(U|B_i) P(B_i)}
where P(U) = \frac{1}{3}( \frac{7}{10}...
\frac{7}{10} \frac{6}{9} denotes the case the 1st drew product is unflawed and the 2nd drew product is also unflawed.
\frac{6}{9} means after the 1st withdrawal there are 9 products left in the Box 1 and 6 of the left products are unflawed
Homework Statement
The manager of a factory proclaims 99% of the products manufactured in his factory are unflawed. If we draw 50 products from 5000 products and find 2 of 50 are flawed, then how do we know the manage is telling the truth?
Homework Equations
Nothing special.
The...
Homework Statement
There are 3 boxes containing some products of same type.
Box 1 contains 10 products and 3 of them are flawed.
Box 2 contains 15 products and 7 of them are flawed.
Box 3 contains 25 products and 5 of them are flawed.
Randomly choose one box from the 3 then draw...
Homework Statement
X is a random variable of binomial distribution of parameter n=10 and unknown parameter p. Hypotheses are given as follows:
H_0 \;\; : \;\; p=0.6
H_1 \;\; : \;\; p \neq 0.6
Suppose rejection region for H_0 is \{X \leq 1\} \cup \{X \geq 9\}
Question 1: What is...
Actually, I have no instructor to consult.
I learned the probability and statistics by reading textbooks and doing exercises in the ends of each chapters.
This may be the only place I can acquire the correct answers with the help of kind people like you and Ray.
Current answer is good enough...
Thank you for reply.
Sorry for causing confusion, "σ is given but unknown" just means although σ remains in the formula, it acts like the unknown variable and needs to be estimated through the known values of X_{1},\; X_{2},\;\;...,\;\; X_{n} .
Thank you for mentioning the M.L.E.
Actually...
Thank you for your replay, Ray.
Actually, the moment estimator denotes the method of moments estimator, you can find it here: http://en.wikipedia.org/wiki/Method_of_moments_(statistics )
What I’m concerning is the estimator found by using method of moments.
Answer 2 is wrong.
It...
Homework Statement
If the probability density function (p.d.f.) of the random variable X is
f(x| \theta ) =\begin{cases} \frac{1}{3\theta} & 0 < x \leq 3\theta
\\0 & otherwise\end{cases}
Where \theta > 0 is an unknown parameter, and X_1, X_2 … X_n is a sample from X where n > 2...